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<div class="headertitle"><div class="title">trust_region.cc</div></div>
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<a href="trust__region_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include "<a class="code" href="trust__region_8h.html">ortools/pdlp/trust_region.h</a>"</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <cmath></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <limits></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <utility></span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "Eigen/Core"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "absl/types/optional.h"</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include "<a class="code" href="mathutil_8h.html">ortools/base/mathutil.h</a>"</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include "<a class="code" href="quadratic__program_8h.html">ortools/pdlp/quadratic_program.h</a>"</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include "<a class="code" href="sharded__optimization__utils_8h.html">ortools/pdlp/sharded_optimization_utils.h</a>"</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#include "<a class="code" href="sharded__quadratic__program_8h.html">ortools/pdlp/sharded_quadratic_program.h</a>"</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor">#include "<a class="code" href="sharder_8h.html">ortools/pdlp/sharder.h</a>"</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research_1_1pdlp.html">operations_research::pdlp</a> {</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span>using ::Eigen::VectorXd;</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// The functions in this file that are templated on a TrustRegionProblem use the</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// templated class to specify the following trust-region problem with bound</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// constraints:</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// min_x Objective' * (x - CenterPoint)</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// s.t. LowerBound <= x <= UpperBound</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// || x - Centerpoint ||_W <= target_radius</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// where ||y||_W = sqrt(sum_i NormWeight[i] * y[i]^2)</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// The templated TrustRegionProblem type should provide methods:</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// double Objective(int64_t index) const;</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// double LowerBound(int64_t index) const;</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// double UpperBound(int64_t index) const;</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// double CenterPoint(int64_t index) const;</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// double NormWeight(int64_t index) const;</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// which give the values of the corresponding terms in the problem</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// specification. See VectorTrustRegionProblem for an example. The</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// *TrustRegionProblem classes below implement several instances of</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// TrustRegionProblem.</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">// On the other hand, the functions that are templated on a</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// DiagonalTrustRegionProblem use the templated class to specify the following</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment">// trust-region problem with bound constraints:</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// min_x (1 / 2) * (x - CenterPoint)' ObjectiveMatrix * (x - CenterPoint)</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">// + Objective' * (x - CenterPoint)</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// s.t. LowerBound <= x <= UpperBound</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// || x - CenterPoint ||_W <= target_radius,</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment">// where ||y||_W = sqrt(sum_i NormWeight[i] * y[i]^2) and ObjectiveMatrix is</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment">// assumed to be a diagonal matrix with nonnegative entries. Templated</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment">// DiagonalTrustRegionProblem types should provide all the methods provided by</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment">// templated TrustRegionProblem types, as well as:</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">// double ObjectiveMatrixDiagonalAt(int64_t index) const;</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">// which gives the value of the objective matrix diagonal at a specified index.</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">// See DiagonalTrustRegionProblemFromQp for an example that sets up the diagonal</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment">// trust region problem from an existing ShardedQuadraticProgram.</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="comment">// VectorTrustRegionProblem uses explicit vectors to define the trust region</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="comment">// problem. It captures const references to the vectors used in the constrcutor,</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment">// which should outlive the class instance.</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="keyword">class </span>VectorTrustRegionProblem {</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> VectorTrustRegionProblem(<span class="keyword">const</span> VectorXd* objective,</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>,</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>,</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>,</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">const</span> VectorXd* norm_weight)</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> : <a class="code hl_variable" href="search_8cc.html#a9c6d2505b571d11bc113813060f465a3">objective_</a>(*objective),</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> lower_bound_(*<a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>),</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> upper_bound_(*<a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>),</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> center_point_(*<a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>),</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> norm_weight_(*norm_weight) {}</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordtype">double</span> Objective(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="search_8cc.html#a9c6d2505b571d11bc113813060f465a3">objective_</a>(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>); }</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a3ad49ae9019c528851f6fd084479a567">LowerBound</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> lower_bound_(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>); }</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a9e815eb2193f1bb6903274c7f0859cd7">UpperBound</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> upper_bound_(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>); }</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordtype">double</span> CenterPoint(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> center_point_(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>); }</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordtype">double</span> NormWeight(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> norm_weight_(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>); }</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="search_8cc.html#a9c6d2505b571d11bc113813060f465a3">objective_</a>;</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">const</span> VectorXd& lower_bound_;</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keyword">const</span> VectorXd& upper_bound_;</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keyword">const</span> VectorXd& center_point_;</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">const</span> VectorXd& norm_weight_;</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span>};</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> </div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// JointTrustRegionProblem defines the joint primal/dual trust region problem</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment">// given a QuadraticProgram, primal and dual solutions, primal and dual</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment">// gradients, and the primal weight. The joint problem (implicitly) concatenates</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="comment">// the primal and dual vectors. The class captures const references to the</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment">// constructor arguments (except primal_weight), which should outlive the class</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="comment">// instance.</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment">// The corresponding trust region problem is</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment">// min primal_gradient' * (x - primal_solution)</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment">// - dual_gradient' * (y - dual_solution)</span></div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="comment">// s.t. qp.variable_lower_bounds <= x <= qp.variable_upper_bounds</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="comment">// qp.implicit_dual_lower_bounds <= y <= qp.implicit_dual_upper_bounds</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="comment">// || (x, y) - (primal_solution, dual_solution) ||_2 <= target_radius</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="comment">// where the implicit dual bounds are those given in</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span><span class="comment">// https://developers.google.com/optimization/lp/pdlp_math#dual_variable_bounds</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="keyword">class </span>JointTrustRegionProblem {</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> JointTrustRegionProblem(<span class="keyword">const</span> QuadraticProgram* qp,</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keyword">const</span> VectorXd* primal_solution,</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keyword">const</span> VectorXd* dual_solution,</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keyword">const</span> VectorXd* primal_gradient,</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">const</span> VectorXd* dual_gradient,</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight)</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> : qp_(*qp),</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> primal_size_(qp_.<a class="code hl_variable" href="trust__region__test_8cc.html#a16346c4c462dec8f0cf38493c5e0358c">variable_lower_bounds</a>.size()),</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> primal_solution_(*primal_solution),</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> dual_solution_(*dual_solution),</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> primal_gradient_(*primal_gradient),</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> dual_gradient_(*dual_gradient),</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> primal_weight_(primal_weight) {}</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordtype">double</span> Objective(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_ ? primal_gradient_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> : -dual_gradient_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> - primal_size_];</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> }</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a3ad49ae9019c528851f6fd084479a567">LowerBound</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_ ? qp_.variable_lower_bounds[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> : std::isfinite(qp_.constraint_upper_bounds[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> - primal_size_])</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> ? -std::numeric_limits<double>::infinity()</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> : 0.0;</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> }</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a9e815eb2193f1bb6903274c7f0859cd7">UpperBound</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_ ? qp_.variable_upper_bounds[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> : std::isfinite(qp_.constraint_lower_bounds[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> - primal_size_])</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> ? std::numeric_limits<double>::infinity()</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> : 0.0;</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keywordtype">double</span> CenterPoint(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_ ? primal_solution_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> : dual_solution_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> - primal_size_];</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> }</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordtype">double</span> NormWeight(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_ ? 0.5 * primal_weight_ : 0.5 / primal_weight_;</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> }</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keyword">const</span> QuadraticProgram& qp_;</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">const</span> int64_t primal_size_;</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">const</span> VectorXd& primal_solution_;</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">const</span> VectorXd& dual_solution_;</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keyword">const</span> VectorXd& primal_gradient_;</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keyword">const</span> VectorXd& dual_gradient_;</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight_;</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span>};</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> </div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="keyword">struct </span>TrustRegionResultStepSize {</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="comment">// The step_size of the solution.</span></div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"><a class="line" href="trust__region_8cc.html#a879215ecd0117ade78436fc4590747e0"> 165</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="trust__region_8cc.html#a879215ecd0117ade78436fc4590747e0">solution_step_size</a>;</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// The value objective_vector' * (solution - center_point).</span></div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"><a class="line" href="trust__region_8cc.html#a69703b8569462134ad4e22ab0133e418"> 167</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="trust__region_8cc.html#a69703b8569462134ad4e22ab0133e418">objective_value</a>;</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span>};</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> </div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="comment">// "problem" is sharded according to the given sharder. Within each shard,</span></div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="comment">// this function selects the subset of elements corresponding to</span></div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="comment">// indexed_components_by_shard, and takes the median of the critical step sizes</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="comment">// of these elements, producing an array A of shard medians. Then returns the</span></div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="comment">// median of the array A. CHECK-fails if indexed_components_by_shard is empty</span></div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span><span class="comment">// for all shards.</span></div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="keywordtype">double</span> MedianOfShardMedians(</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keyword">const</span> TrustRegionProblem& problem,</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keyword">const</span> std::vector<std::vector<int64_t>>& indexed_components_by_shard,</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keyword">const</span> Sharder& sharder) {</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> std::vector<absl::optional<double>> shard_medians(sharder.NumShards(),</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> absl::nullopt);</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keyword">const</span> <span class="keyword">auto</span>& indexed_shard_components =</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> indexed_components_by_shard[shard.Index()];</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordflow">if</span> (!indexed_shard_components.empty()) {</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> shard_medians[shard.Index()] = internal::EasyMedian(</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> indexed_shard_components, [&](const int64_t index) {</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> return internal::CriticalStepSize(problem, index);</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> });</div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> }</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> });</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> std::vector<double> non_empty_medians;</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& median : shard_medians) {</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keywordflow">if</span> (median.has_value()) {</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> non_empty_medians.push_back(*median);</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> }</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> }</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(!non_empty_medians.empty());</div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#ab8901158cf75681cf82a1d866a1118e6">internal::EasyMedian</a>(non_empty_medians,</div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> x; });</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span>}</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> </div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span><span class="keyword">struct </span>InitialState {</div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"><a class="line" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6"> 205</a></span> std::vector<std::vector<int64_t>> <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>;</div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"><a class="line" href="trust__region_8cc.html#a9f97b60109cf3b1650acf7fa8b5dd307"> 206</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="trust__region_8cc.html#a9f97b60109cf3b1650acf7fa8b5dd307">radius_coefficient_of_decided_components</a>;</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span>};</div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> </div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span>InitialState ComputeInitialState(<span class="keyword">const</span> TrustRegionProblem& problem,</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keyword">const</span> Sharder& sharder) {</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> InitialState result;</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> result.undecided_components_by_shard.resize(sharder.NumShards());</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> result.radius_coefficient_of_decided_components =</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> sharder.ParallelSumOverShards([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keyword">const</span> int64_t shard_start = sharder.ShardStart(shard.Index());</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">const</span> int64_t shard_size = sharder.ShardSize(shard.Index());</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a0d1a488cd88b2db320196184c8a60713">internal::ComputeInitialUndecidedComponents</a>(</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> problem, shard_start, shard_start + shard_size,</div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> result.undecided_components_by_shard[shard.Index()]);</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> });</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span>}</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#af260cca7eeddd5e8e77712bd259b3278">RadiusSquaredOfUndecidedComponents</a>(</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="keyword">const</span> TrustRegionProblem& problem, <span class="keyword">const</span> <span class="keywordtype">double</span> step_size,</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keyword">const</span> Sharder& sharder,</div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keyword">const</span> std::vector<std::vector<int64_t>>& <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) {</div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keywordflow">return</span> sharder.ParallelSumOverShards([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#af260cca7eeddd5e8e77712bd259b3278">internal::RadiusSquaredOfUndecidedComponents</a>(</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> problem, step_size, <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>[shard.Index()]);</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> });</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span>}</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> </div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a7d3c6d3cc8d588acbb2573e3384f3bd0">RemoveCriticalStepsAboveThreshold</a>(</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">const</span> TrustRegionProblem& problem, <span class="keyword">const</span> <span class="keywordtype">double</span> step_size_threshold,</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keyword">const</span> Sharder& sharder,</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> std::vector<std::vector<int64_t>>& <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) {</div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordflow">return</span> sharder.ParallelSumOverShards([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a7d3c6d3cc8d588acbb2573e3384f3bd0">internal::RemoveCriticalStepsAboveThreshold</a>(</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> problem, step_size_threshold,</div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>[shard.Index()]);</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> });</div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span>}</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> </div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#aa8ad95f3ab1aca8e985d46d0db21e15f">RemoveCriticalStepsBelowThreshold</a>(</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keyword">const</span> TrustRegionProblem& problem, <span class="keyword">const</span> <span class="keywordtype">double</span> step_size_threshold,</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keyword">const</span> Sharder& sharder,</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> std::vector<std::vector<int64_t>>& <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) {</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keywordflow">return</span> sharder.ParallelSumOverShards([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#aa8ad95f3ab1aca8e985d46d0db21e15f">internal::RemoveCriticalStepsBelowThreshold</a>(</div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> problem, step_size_threshold,</div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>[shard.Index()]);</div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> });</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span>}</div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> </div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span>int64_t NumUndecidedComponents(</div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="keyword">const</span> std::vector<std::vector<int64_t>>& <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) {</div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> int64_t num_undecided_components = 0;</div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& undecided_components : <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) {</div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> num_undecided_components += undecided_components.size();</div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> }</div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="keywordflow">return</span> num_undecided_components;</div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span>}</div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> </div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span>int64_t MaxUndecidedComponentsInAnyShard(</div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="keyword">const</span> std::vector<std::vector<int64_t>>& <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) {</div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> int64_t <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = 0;</div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& undecided_components : <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) {</div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = std::max<int64_t>(<a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>, undecided_components.size());</div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> }</div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>;</div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span>}</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> </div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span>VectorXd ComputeSolution(<span class="keyword">const</span> TrustRegionProblem& problem,</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="keyword">const</span> <span class="keywordtype">double</span> step_size, <span class="keyword">const</span> Sharder& sharder) {</div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> VectorXd solution(sharder.NumElements());</div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keyword">const</span> int64_t shard_start = sharder.ShardStart(shard.Index());</div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="keyword">const</span> int64_t shard_size = sharder.ShardSize(shard.Index());</div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> for (int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> = shard_start; <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < shard_start + shard_size;</div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> ++<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) {</div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> solution[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>] = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a70dfeb22c2d7bf7aac11a168f80d8bb1">internal::ProjectedValue</a>(problem, <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>, step_size);</div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> }</div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> });</div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="keywordflow">return</span> solution;</div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span>}</div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> </div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#abb66766a5d79e878ff67851bc55ca24f">ComputeObjectiveValue</a>(<span class="keyword">const</span> TrustRegionProblem& problem,</div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="keyword">const</span> <span class="keywordtype">double</span> step_size, <span class="keyword">const</span> Sharder& sharder) {</div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keywordflow">return</span> sharder.ParallelSumOverShards([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="keyword">const</span> int64_t shard_start = sharder.ShardStart(shard.Index());</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <span class="keyword">const</span> int64_t shard_size = sharder.ShardSize(shard.Index());</div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> <span class="keywordtype">double</span> shard_value = 0.0;</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> for (int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> = shard_start; <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < shard_start + shard_size;</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> ++<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) {</div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> shard_value += problem.Objective(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) *</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> (<a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a70dfeb22c2d7bf7aac11a168f80d8bb1">internal::ProjectedValue</a>(problem, <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>, step_size) -</div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> problem.CenterPoint(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>));</div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> }</div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keywordflow">return</span> shard_value;</div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> });</div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span>}</div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> </div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span><span class="comment">// Solves the following trust-region problem with bound constraints:</span></div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span><span class="comment">// min_x Objective' * (x - CenterPoint)</span></div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span><span class="comment">// s.t. LowerBound <= x <= UpperBound</span></div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span><span class="comment">// || x - Centerpoint ||_W <= target_radius</span></div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span><span class="comment">// where ||y||_W = sqrt(sum_i NormWeight[i] * y[i]^2)</span></div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span><span class="comment">// given by a TrustRegionProblem (see description at the top of this file),</span></div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span><span class="comment">// using an exact linear-time method. The sharder's size is used to determine</span></div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span><span class="comment">// the size of the problem. Assumes that there is always a feasible solution,</span></div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span><span class="comment">// that is, that problem.LowerBound(i) <= problem.CenterPoint(i) <=</span></div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span><span class="comment">// problem.UpperBound(i), and that problem.NormWeight(i) > 0, for</span></div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span><span class="comment">// 0 <= i < sharder.NumElements().</span></div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span><span class="comment">//</span></div>
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span><span class="comment">// The linear-time method is based on the observation that the optimal x will be</span></div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span><span class="comment">// of the form x(delta) =</span></div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span><span class="comment">// proj(center_point - delta * objective_vector / norm_weights, bounds)</span></div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span><span class="comment">// for some delta such that || x(delta) - center_point ||_W = target_radius</span></div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span><span class="comment">// (except for corner cases where the radius constraint is inactive) and the</span></div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span><span class="comment">// vector division is element-wise. Therefore we find the critical threshold for</span></div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span><span class="comment">// each coordinate, and repeatedly: (1) take the median delta, (2) check the</span></div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span><span class="comment">// corresponding radius, and (3) eliminate half of the data points from</span></div>
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span><span class="comment">// consideration.</span></div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span>TrustRegionResultStepSize SolveTrustRegionStepSize(</div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> <span class="keyword">const</span> TrustRegionProblem& problem, <span class="keyword">const</span> <span class="keywordtype">double</span> target_radius,</div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <span class="keyword">const</span> Sharder& sharder) {</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> <a class="code hl_define" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(target_radius, 0.0);</div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> </div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> norm_weights_are_positive =</div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> sharder.ParallelTrueForAllShards([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="keyword">const</span> int64_t shard_start = sharder.ShardStart(shard.Index());</div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <span class="keyword">const</span> int64_t shard_size = sharder.ShardSize(shard.Index());</div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> for (int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> = shard_start; <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < shard_start + shard_size;</div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> ++<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) {</div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <span class="keywordflow">if</span> (problem.NormWeight(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) <= 0.0) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> }</div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> });</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(norm_weights_are_positive);</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> </div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> <span class="keywordflow">if</span> (target_radius == 0.0) {</div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <span class="keywordflow">return</span> {.solution_step_size = 0.0, .objective_value = 0.0};</div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> }</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> </div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> objective_is_all_zeros =</div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> sharder.ParallelTrueForAllShards([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="keyword">const</span> int64_t shard_start = sharder.ShardStart(shard.Index());</div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="keyword">const</span> int64_t shard_size = sharder.ShardSize(shard.Index());</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> for (int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> = shard_start; <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < shard_start + shard_size;</div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> ++<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) {</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <span class="keywordflow">if</span> (problem.Objective(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) != 0.0) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> }</div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> });</div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> <span class="keywordflow">if</span> (objective_is_all_zeros) {</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> <span class="keywordflow">return</span> {.solution_step_size = 0.0, .objective_value = 0.0};</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> }</div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> </div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> InitialState initial_state = ComputeInitialState(problem, sharder);</div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> </div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> <span class="comment">// The contribution to the weighted radius squared from the variables that we</span></div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="comment">// know are at their bounds in the solution.</span></div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="keywordtype">double</span> fixed_radius_squared = 0.0;</div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> </div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> <span class="comment">// This value times step_size^2 gives the contribution to the weighted radius</span></div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> <span class="comment">// squared from the variables determined in the solution by the formula</span></div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <span class="comment">// center_point - step_size * objective / norm_weights. These variables are</span></div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="comment">// not at their bounds in the solution, except in degenerate cases.</span></div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> <span class="keywordtype">double</span> variable_radius_coefficient =</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> initial_state.radius_coefficient_of_decided_components;</div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> </div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="comment">// For each shard, the components of the variables that aren't accounted for</span></div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> <span class="comment">// in fixed_radius_squared or variable_radius_coefficient, i.e., we don't know</span></div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> <span class="comment">// if they're at their bounds in the solution.</span></div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> std::vector<std::vector<int64_t>> <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>(</div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> std::move(initial_state.undecided_components_by_shard));</div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> </div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> <span class="comment">// These are counters for the number of variables we inspect overall during</span></div>
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<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> <span class="comment">// the solve, including in the initialization. The "worst case" accounts for</span></div>
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<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <span class="comment">// imbalance across the shards by charging each round for the maximum number</span></div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> <span class="comment">// of elements in a shard, because shards with fewer elements may correspond</span></div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <span class="comment">// to idle threads.</span></div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> int64_t actual_elements_seen = sharder.NumElements();</div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> int64_t worst_case_elements_seen = sharder.NumElements();</div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> </div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> <span class="keywordflow">while</span> (NumUndecidedComponents(<a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) > 0) {</div>
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<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> worst_case_elements_seen +=</div>
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<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> MaxUndecidedComponentsInAnyShard(<a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>) *</div>
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<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> sharder.NumShards();</div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> actual_elements_seen +=</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> NumUndecidedComponents(<a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>);</div>
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<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> </div>
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<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <span class="keyword">const</span> <span class="keywordtype">double</span> step_size_threshold =</div>
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<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> MedianOfShardMedians(problem, <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>, sharder);</div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> <span class="keyword">const</span> <span class="keywordtype">double</span> radius_squared_of_undecided_components =</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#af260cca7eeddd5e8e77712bd259b3278">RadiusSquaredOfUndecidedComponents</a>(</div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> problem, <span class="comment">/*step_size=*/</span>step_size_threshold, sharder,</div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>);</div>
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<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> </div>
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<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> <span class="keyword">const</span> <span class="keywordtype">double</span> radius_squared_at_threshold =</div>
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<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> radius_squared_of_undecided_components + fixed_radius_squared +</div>
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<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> variable_radius_coefficient * <a class="code hl_function" href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">MathUtil::Square</a>(step_size_threshold);</div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> </div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> <span class="keywordflow">if</span> (radius_squared_at_threshold > <a class="code hl_function" href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">MathUtil::Square</a>(target_radius)) {</div>
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<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> variable_radius_coefficient += <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a7d3c6d3cc8d588acbb2573e3384f3bd0">RemoveCriticalStepsAboveThreshold</a>(</div>
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<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> problem, step_size_threshold, sharder, <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>);</div>
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<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> fixed_radius_squared += <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#aa8ad95f3ab1aca8e985d46d0db21e15f">RemoveCriticalStepsBelowThreshold</a>(</div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> problem, step_size_threshold, sharder, <a class="code hl_variable" href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a>);</div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> }</div>
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<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> }</div>
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<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Total passes through variables: "</span></div>
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<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> << actual_elements_seen / <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(sharder.NumElements());</div>
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<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Theoretical slowdown because of shard imbalance: "</span></div>
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<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> << <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(worst_case_elements_seen) /</div>
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<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> actual_elements_seen -</div>
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<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> 1.0;</div>
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<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> </div>
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<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> <span class="comment">// Now that we know exactly which variables are fixed at their bounds,</span></div>
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<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> <span class="comment">// compute the step size that will give us the exact target radius.</span></div>
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> <span class="comment">// This is the solution to: fixed_radius_squared +</span></div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <span class="comment">// variable_radius_coefficient * step_size^2 == target_radius^2.</span></div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> <span class="keywordtype">double</span> step_size = 0.0;</div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="keywordflow">if</span> (variable_radius_coefficient > 0.0) {</div>
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<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> step_size =</div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> std::sqrt((<a class="code hl_function" href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">MathUtil::Square</a>(target_radius) - fixed_radius_squared) /</div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> variable_radius_coefficient);</div>
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<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="comment">// All variables are fixed at their bounds. So we can take a very large</span></div>
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<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <span class="comment">// finite step. We don't use infinity as the step in order to avoid 0 *</span></div>
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<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> <span class="comment">// infinity = NaN when zeros are present in the objective vector. It's ok if</span></div>
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<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> <span class="comment">// the result of step_size * objective_vector has infinity components</span></div>
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<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> <span class="comment">// because these are projected correctly to bounds.</span></div>
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<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> step_size = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<double>::max</a>();</div>
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<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> }</div>
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<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> </div>
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<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> <span class="keywordflow">return</span> {</div>
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<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> .solution_step_size = step_size,</div>
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<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> .objective_value = <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#abb66766a5d79e878ff67851bc55ca24f">ComputeObjectiveValue</a>(problem, step_size, sharder)};</div>
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<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span>}</div>
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<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> </div>
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<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span>} <span class="comment">// namespace</span></div>
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<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> </div>
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<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a8da80544adc685ee442522ede0e095a9"> 452</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html">TrustRegionResult</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a8da80544adc685ee442522ede0e095a9">SolveTrustRegion</a>(<span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#ac824522e23b1d307c272d07493af3a65">objective_vector</a>,</div>
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<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#a16346c4c462dec8f0cf38493c5e0358c">variable_lower_bounds</a>,</div>
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<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#a868af74445e29f368ccf4a9e053f9267">variable_upper_bounds</a>,</div>
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<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>,</div>
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<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#ad31783425c63eac33cc6aade41a6537d">norm_weights</a>,</div>
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<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> <span class="keyword">const</span> <span class="keywordtype">double</span> target_radius,</div>
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<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a>& sharder) {</div>
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<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> VectorTrustRegionProblem problem(&<a class="code hl_variable" href="trust__region__test_8cc.html#ac824522e23b1d307c272d07493af3a65">objective_vector</a>, &<a class="code hl_variable" href="trust__region__test_8cc.html#a16346c4c462dec8f0cf38493c5e0358c">variable_lower_bounds</a>,</div>
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<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> &<a class="code hl_variable" href="trust__region__test_8cc.html#a868af74445e29f368ccf4a9e053f9267">variable_upper_bounds</a>, &<a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>,</div>
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<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> &<a class="code hl_variable" href="trust__region__test_8cc.html#ad31783425c63eac33cc6aade41a6537d">norm_weights</a>);</div>
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<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> TrustRegionResultStepSize solution =</div>
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<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> SolveTrustRegionStepSize(problem, target_radius, sharder);</div>
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<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <span class="keywordflow">return</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html">TrustRegionResult</a>{</div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> .<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a879215ecd0117ade78436fc4590747e0">solution_step_size</a> = solution.solution_step_size,</div>
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<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> .objective_value = solution.objective_value,</div>
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<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> .solution =</div>
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<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> ComputeSolution(problem, solution.solution_step_size, sharder),</div>
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<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> };</div>
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<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span>}</div>
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<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> </div>
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<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span><span class="comment">// A generic trust region problem of the form:</span></div>
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<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span><span class="comment">// min_{x} (1 / 2) * (x - center_point)'Q(x - center_point)</span></div>
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<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span><span class="comment">// + c'(x - center_point)</span></div>
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<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span><span class="comment">// s.t. l <= (x - center_point) <= u</span></div>
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<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span><span class="comment">// ||x - center_point||_W <= radius</span></div>
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<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span><span class="comment">// where ||z||_W = sqrt(sum_i w_i z_i^2) is a weighted Euclidean norm.</span></div>
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<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span><span class="comment">// It is assumed that the objective matrix Q is a nonnegative diagonal matrix.</span></div>
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<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html"> 479</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html">DiagonalTrustRegionProblem</a> {</div>
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<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> <span class="comment">// A reference to the objects passed in the constructor is kept, so they must</span></div>
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<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> <span class="comment">// outlive the DiagonalTrustRegionProblem instance.</span></div>
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<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a738219be743444c6ffc6fdb9802ab5a3"> 483</a></span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a738219be743444c6ffc6fdb9802ab5a3">DiagonalTrustRegionProblem</a>(<span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="trust__region__test_8cc.html#ac824522e23b1d307c272d07493af3a65">objective_vector</a>,</div>
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<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> <span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="trust__region__test_8cc.html#ad8dc72e7835d167fffffac5769c55076">objective_matrix_diagonal</a>,</div>
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<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> <span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a>,</div>
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<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> <span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a>,</div>
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<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> <span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>,</div>
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<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> <span class="keyword">const</span> VectorXd* <a class="code hl_variable" href="trust__region__test_8cc.html#ad31783425c63eac33cc6aade41a6537d">norm_weights</a>)</div>
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<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> : objective_vector_(*<a class="code hl_variable" href="trust__region__test_8cc.html#ac824522e23b1d307c272d07493af3a65">objective_vector</a>),</div>
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<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> objective_matrix_diagonal_(*<a class="code hl_variable" href="trust__region__test_8cc.html#ad8dc72e7835d167fffffac5769c55076">objective_matrix_diagonal</a>),</div>
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<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> variable_lower_bounds_(*<a class="code hl_variable" href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a>),</div>
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<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> variable_upper_bounds_(*<a class="code hl_variable" href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a>),</div>
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<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> center_point_(*<a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>),</div>
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<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> norm_weight_(*<a class="code hl_variable" href="trust__region__test_8cc.html#ad31783425c63eac33cc6aade41a6537d">norm_weights</a>) {}</div>
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<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> </div>
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<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a745a6cbad664d808756705f7c7920754"> 496</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a745a6cbad664d808756705f7c7920754">CenterPoint</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> center_point_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]; }</div>
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<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> </div>
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<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#adbf3f8e0abf2f5206e3eea73a37ad6cd"> 498</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#adbf3f8e0abf2f5206e3eea73a37ad6cd">NormWeight</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> norm_weight_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]; }</div>
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<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> </div>
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<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a3a130beba19f9a43060251fc0b031330"> 500</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a3a130beba19f9a43060251fc0b031330">LowerBound</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> <span class="keywordflow">return</span> variable_lower_bounds_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>];</div>
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<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> }</div>
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<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> </div>
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<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3"> 504</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3">UpperBound</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> <span class="keywordflow">return</span> variable_upper_bounds_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>];</div>
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<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> }</div>
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<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> </div>
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<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a09ccf99be502491aacb4aa87583d2bdd"> 508</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a09ccf99be502491aacb4aa87583d2bdd">Objective</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> objective_vector_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]; }</div>
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<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> </div>
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<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a2e2de156de8d096f7491fb76053a2289"> 510</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a2e2de156de8d096f7491fb76053a2289">ObjectiveMatrixDiagonalAt</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> <span class="keywordflow">return</span> objective_matrix_diagonal_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>];</div>
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<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> }</div>
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<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> </div>
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<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> <span class="keyword">const</span> VectorXd& objective_vector_;</div>
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<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span> <span class="keyword">const</span> VectorXd& objective_matrix_diagonal_;</div>
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<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> <span class="keyword">const</span> VectorXd& variable_lower_bounds_;</div>
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<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> <span class="keyword">const</span> VectorXd& variable_upper_bounds_;</div>
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<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> <span class="keyword">const</span> VectorXd& center_point_;</div>
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<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> <span class="keyword">const</span> VectorXd& norm_weight_;</div>
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<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span>};</div>
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<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> </div>
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<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span><span class="comment">// DiagonalTrustRegionProblemFromQp accepts a diagonal quadratic program and</span></div>
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<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span><span class="comment">// information about the current solution and gradient and sets up the following</span></div>
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<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span><span class="comment">// trust-region subproblem:</span></div>
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<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span><span class="comment">// min_{x, y} (x - primal_solution)'Q(x - primal_solution)</span></div>
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<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span><span class="comment">// + primal_gradient'(x - primal_solution)</span></div>
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<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span><span class="comment">// - dual_gradient'(y - dual_solution)</span></div>
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<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span><span class="comment">// s.t. l <= x - primal_solution <= u</span></div>
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<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span><span class="comment">// l_implicit <= y - dual_solution <= u_implicit</span></div>
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<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span><span class="comment">// ||(x, y) - (primal_solution, dual_solution)||_W <= r,</span></div>
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<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span><span class="comment">// where</span></div>
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<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span><span class="comment">// ||(x, y)||_W = sqrt(0.5 * primal_weight ||x||^2 +</span></div>
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<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span><span class="comment">// (0.5 / primal_weight) ||y||^2).</span></div>
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<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span><span class="comment">// This class implements the same methods as DiagonalTrustRegionProblem, but</span></div>
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<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span><span class="comment">// without the need to explicitly copy vectors.</span></div>
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<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html"> 537</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html">DiagonalTrustRegionProblemFromQp</a> {</div>
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<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> <span class="comment">// A reference to the objects passed in the constructor is kept, so they must</span></div>
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<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> <span class="comment">// outlive the DiagonalTrustRegionProblemFromQp instance.</span></div>
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<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a52ee25b9d65144642b73c47107026f37"> 541</a></span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a52ee25b9d65144642b73c47107026f37">DiagonalTrustRegionProblemFromQp</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a>* qp,</div>
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<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> <span class="keyword">const</span> VectorXd* primal_solution,</div>
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<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> <span class="keyword">const</span> VectorXd* dual_solution,</div>
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<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> <span class="keyword">const</span> VectorXd* primal_gradient,</div>
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<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span> <span class="keyword">const</span> VectorXd* dual_gradient,</div>
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<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight)</div>
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<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span> : qp_(*qp),</div>
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<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> primal_solution_(*primal_solution),</div>
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<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> dual_solution_(*dual_solution),</div>
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<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> primal_gradient_(*primal_gradient),</div>
|
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<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span> dual_gradient_(*dual_gradient),</div>
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<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> primal_size_(primal_solution->size()),</div>
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<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> primal_weight_(primal_weight) {}</div>
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<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> </div>
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<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a745a6cbad664d808756705f7c7920754"> 555</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a745a6cbad664d808756705f7c7920754">CenterPoint</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_) ? primal_solution_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]</div>
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<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> : dual_solution_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> - primal_size_];</div>
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<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> }</div>
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<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> </div>
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<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#adbf3f8e0abf2f5206e3eea73a37ad6cd"> 560</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#adbf3f8e0abf2f5206e3eea73a37ad6cd">NormWeight</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_) ? 0.5 * primal_weight_ : 0.5 / primal_weight_;</div>
|
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<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> }</div>
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<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> </div>
|
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<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a3a130beba19f9a43060251fc0b031330"> 564</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a3a130beba19f9a43060251fc0b031330">LowerBound</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_) {</div>
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<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span> <span class="keywordflow">return</span> qp_.variable_lower_bounds[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>];</div>
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<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> <span class="keywordflow">return</span> std::isfinite(qp_.constraint_upper_bounds[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> - primal_size_])</div>
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<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> ? -std::numeric_limits<double>::infinity()</div>
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<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> : 0.0;</div>
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<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> }</div>
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<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> }</div>
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<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> </div>
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<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3"> 574</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3">UpperBound</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_) {</div>
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<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> <span class="keywordflow">return</span> qp_.variable_upper_bounds[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>];</div>
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<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> <span class="keywordflow">return</span> std::isfinite(qp_.constraint_lower_bounds[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> - primal_size_])</div>
|
|
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> ? std::numeric_limits<double>::infinity()</div>
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|
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> : 0.0;</div>
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<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> }</div>
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<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> }</div>
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<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> </div>
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<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a09ccf99be502491aacb4aa87583d2bdd"> 584</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a09ccf99be502491aacb4aa87583d2bdd">Objective</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_) ? primal_gradient_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]</div>
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<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> : -dual_gradient_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> - primal_size_];</div>
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<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> }</div>
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<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> </div>
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<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a2e2de156de8d096f7491fb76053a2289"> 589</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a2e2de156de8d096f7491fb76053a2289">ObjectiveMatrixDiagonalAt</a>(int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> <span class="keywordflow">if</span> (qp_.objective_matrix.has_value()) {</div>
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<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < primal_size_) ? qp_.objective_matrix->diagonal()[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]</div>
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<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> : 0.0;</div>
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<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> <span class="keywordflow">return</span> 0.0;</div>
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<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> }</div>
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<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> }</div>
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<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> </div>
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<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a>& qp_;</div>
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<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> <span class="keyword">const</span> VectorXd& primal_solution_;</div>
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<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> <span class="keyword">const</span> VectorXd& dual_solution_;</div>
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<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> <span class="keyword">const</span> VectorXd& primal_gradient_;</div>
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<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> <span class="keyword">const</span> VectorXd& dual_gradient_;</div>
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<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> <span class="keyword">const</span> int64_t primal_size_;</div>
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<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight_;</div>
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<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span>};</div>
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<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> </div>
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<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span><span class="comment">// Computes a single coordinate projection of the scaled difference,</span></div>
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<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span><span class="comment">// sqrt(NormWeight(i)) * (x[i] - CenterPoint(i)), to the corresponding box</span></div>
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<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span><span class="comment">// constraints. As a function of scaling_factor, the difference is equal to</span></div>
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<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span><span class="comment">// (Q[i, i] / NormWeight(i)) + scaling_factor)^{-1} *</span></div>
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<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span><span class="comment">// (-c[i] / sqrt(NormWeight(i))),</span></div>
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<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span><span class="comment">// where Q, c are the objective matrix and vector, respectively.</span></div>
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<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span><span class="keyword">template</span> <<span class="keyword">typename</span> DiagonalTrustRegionProblem></div>
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<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#accb6df46237b5d870b93c6566cadd722"> 615</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#accb6df46237b5d870b93c6566cadd722">ProjectedValueOfScaledDifference</a>(</div>
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<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html">DiagonalTrustRegionProblem</a>& problem, <span class="keyword">const</span> int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>,</div>
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<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> <span class="keyword">const</span> <span class="keywordtype">double</span> scaling_factor) {</div>
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<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a> = problem.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#adbf3f8e0abf2f5206e3eea73a37ad6cd">NormWeight</a>(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(</div>
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<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>((-problem.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a09ccf99be502491aacb4aa87583d2bdd">Objective</a>(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) / std::sqrt(<a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a>)) /</div>
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<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> (problem.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a2e2de156de8d096f7491fb76053a2289">ObjectiveMatrixDiagonalAt</a>(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) / <a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a> +</div>
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<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> scaling_factor),</div>
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<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> std::sqrt(<a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a>) *</div>
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<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span> (problem.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a3a130beba19f9a43060251fc0b031330">LowerBound</a>(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) - problem.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a745a6cbad664d808756705f7c7920754">CenterPoint</a>(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>))),</div>
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<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> std::sqrt(<a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a>) *</div>
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<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span> (problem.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3">UpperBound</a>(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) - problem.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a745a6cbad664d808756705f7c7920754">CenterPoint</a>(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)));</div>
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<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span>}</div>
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<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span> </div>
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<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span><span class="comment">// Computes the norm of the projection of the difference vector,</span></div>
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<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span><span class="comment">// x - center_point, to the corresponding box constraints. We are using the</span></div>
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<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span><span class="comment">// standard Euclidean norm (instead of the weighted norm) because the solver</span></div>
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<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span><span class="comment">// implicitly reformulates the problem to one with a Euclidean ball constraint</span></div>
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<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span><span class="comment">// first.</span></div>
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<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span><span class="keyword">template</span> <<span class="keyword">typename</span> DiagonalTrustRegionProblem></div>
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<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a3c71f00da2c898c481414c3e92f12f0d"> 635</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a3c71f00da2c898c481414c3e92f12f0d">NormOfDeltaProjection</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html">DiagonalTrustRegionProblem</a>& problem,</div>
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<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a>& sharder,</div>
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<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> <span class="keyword">const</span> <span class="keywordtype">double</span> scaling_factor) {</div>
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<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> <span class="keyword">const</span> <span class="keywordtype">double</span> squared_norm =</div>
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<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span> sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a2e06481a59fc1f866bd6c898a696b014">ParallelSumOverShards</a>([&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span> <span class="keyword">const</span> int64_t shard_start = sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#abfb02437c97584ca43c040284aecf748">ShardStart</a>(shard.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">Index</a>());</div>
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<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span> <span class="keyword">const</span> int64_t shard_end =</div>
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<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"> 642</span> shard_start + sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a998aef9096f234a37e58caddca6db203">ShardSize</a>(shard.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">Index</a>());</div>
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<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span> <span class="keywordtype">double</span> sum = 0.0;</div>
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<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span> for (int64_t i = shard_start; i < shard_end; ++i) {</div>
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<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span> <span class="keyword">const</span> <span class="keywordtype">double</span> projected_coordinate =</div>
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<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#accb6df46237b5d870b93c6566cadd722">ProjectedValueOfScaledDifference</a>(problem, i, scaling_factor);</div>
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<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span> sum += <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">MathUtil::Square</a>(projected_coordinate);</div>
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<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"> 648</span> }</div>
|
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<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span> <span class="keywordflow">return</span> sum;</div>
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<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span> });</div>
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<div class="line"><a id="l00651" name="l00651"></a><span class="lineno"> 651</span> <span class="keywordflow">return</span> std::sqrt(squared_norm);</div>
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<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"> 652</span>}</div>
|
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<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> </div>
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<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span><span class="comment">// Finds an approximately optimal scaling factor for the solution of the trust</span></div>
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<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span><span class="comment">// region subproblem, which can be passed on to ProjectedCoordinate() to find</span></div>
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<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span><span class="comment">// an approximately optimal solution to the trust region subproblem. The value</span></div>
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<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span><span class="comment">// returned is guaranteed to be within `solve_tol * max(1, s*)` of the optimal</span></div>
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<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span><span class="comment">// scaling `s*`.</span></div>
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<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span><span class="comment">// TODO(user): figure out what accuracy is useful to callers and redo the</span></div>
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<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span><span class="comment">// stopping criterion accordingly.</span></div>
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<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span><span class="keyword">template</span> <<span class="keyword">typename</span> DiagonalTrustRegionProblem></div>
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<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a7bd16384c5572b001a57e9987bf5b0e9"> 662</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a7bd16384c5572b001a57e9987bf5b0e9">FindScalingFactor</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html">DiagonalTrustRegionProblem</a>& problem,</div>
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<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a>& sharder, <span class="keyword">const</span> <span class="keywordtype">double</span> target_radius,</div>
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<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> <span class="keyword">const</span> <span class="keywordtype">double</span> solve_tol) {</div>
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<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> <span class="comment">// Determine a search interval using monotonicity of the squared norm of the</span></div>
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<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> <span class="comment">// candidate solution with respect to the scaling factor.</span></div>
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<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span> <span class="keywordtype">double</span> scaling_factor_lower_bound = 0.0;</div>
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<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span> <span class="keywordtype">double</span> scaling_factor_upper_bound = 1.0;</div>
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<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> <span class="keywordflow">while</span> (<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a3c71f00da2c898c481414c3e92f12f0d">NormOfDeltaProjection</a>(problem, sharder, scaling_factor_upper_bound) >=</div>
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<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span> target_radius) {</div>
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<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> scaling_factor_lower_bound = scaling_factor_upper_bound;</div>
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<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</span> scaling_factor_upper_bound *= 2;</div>
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<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> }</div>
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<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span> <span class="comment">// Invariant: bounds.upper_bound >= bounds.lower_bound.</span></div>
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<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> <span class="keywordflow">while</span> ((scaling_factor_upper_bound - scaling_factor_lower_bound) >=</div>
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<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span> solve_tol * <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(1.0, scaling_factor_lower_bound)) {</div>
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<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> <span class="keyword">const</span> <span class="keywordtype">double</span> middle =</div>
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<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</span> (scaling_factor_lower_bound + scaling_factor_upper_bound) / 2.0;</div>
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<div class="line"><a id="l00679" name="l00679"></a><span class="lineno"> 679</span> <span class="comment">// Norm is monotonically non-increasing as a function of scaling_factor.</span></div>
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<div class="line"><a id="l00680" name="l00680"></a><span class="lineno"> 680</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a3c71f00da2c898c481414c3e92f12f0d">NormOfDeltaProjection</a>(problem, sharder, middle) <= target_radius) {</div>
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<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</span> scaling_factor_upper_bound = middle;</div>
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<div class="line"><a id="l00682" name="l00682"></a><span class="lineno"> 682</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span> scaling_factor_lower_bound = middle;</div>
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<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> }</div>
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<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> }</div>
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<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> <span class="keywordflow">return</span> (scaling_factor_upper_bound + scaling_factor_lower_bound) / 2.0;</div>
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<div class="line"><a id="l00687" name="l00687"></a><span class="lineno"> 687</span>}</div>
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<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> </div>
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<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span><span class="comment">// Solves the diagonal trust region problem using a binary search algorithm.</span></div>
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<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span><span class="comment">// See comment above SolveDiagonalTrustRegion() in trust_region.h for the</span></div>
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<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span><span class="comment">// meaning of solve_tol.</span></div>
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<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span><span class="keyword">template</span> <<span class="keyword">typename</span> DiagonalTrustRegionProblem></div>
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<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a39db3ccea12adec49816af128a288223"> 693</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html">TrustRegionResult</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a39db3ccea12adec49816af128a288223">SolveDiagonalTrustRegionProblem</a>(</div>
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<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html">DiagonalTrustRegionProblem</a>& problem, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a>& sharder,</div>
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<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span> <span class="keyword">const</span> <span class="keywordtype">double</span> target_radius, <span class="keyword">const</span> <span class="keywordtype">double</span> solve_tol) {</div>
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<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span> <a class="code hl_define" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(target_radius, 0.0);</div>
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<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> norm_weights_are_positive =</div>
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<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span> sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a9761cf0a21e5b7efe9126765eec48a3a">ParallelTrueForAllShards</a>([&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span> <span class="keyword">const</span> int64_t shard_start = sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#abfb02437c97584ca43c040284aecf748">ShardStart</a>(shard.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">Index</a>());</div>
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<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span> for (int64_t i = shard_start;</div>
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<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"> 701</span> i < shard_start + sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a998aef9096f234a37e58caddca6db203">ShardSize</a>(shard.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">Index</a>()); ++i) {</div>
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<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span> if (problem.NormWeight(i) <= 0) {</div>
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<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span> return false;</div>
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<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span> }</div>
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<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> }</div>
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|
<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"> 706</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> });</div>
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<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(norm_weights_are_positive);</div>
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<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"> 709</span> <span class="keyword">const</span> <span class="keywordtype">double</span> optimal_scaling =</div>
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<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a7bd16384c5572b001a57e9987bf5b0e9">FindScalingFactor</a>(problem, sharder, target_radius, solve_tol);</div>
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<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> VectorXd solution(sharder.NumElements());</div>
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<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span> <span class="keyword">const</span> int64_t shard_start = sharder.ShardStart(shard.Index());</div>
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<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> <span class="keyword">const</span> int64_t shard_size = sharder.ShardSize(shard.Index());</div>
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<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> for (int64_t i = shard_start; i < shard_start + shard_size; ++i) {</div>
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<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a> = problem.NormWeight(i);</div>
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<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> <span class="keyword">const</span> <span class="keywordtype">double</span> projected_value =</div>
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<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#accb6df46237b5d870b93c6566cadd722">ProjectedValueOfScaledDifference</a>(problem, i, optimal_scaling);</div>
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<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span> solution[i] =</div>
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<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> problem.CenterPoint(i) + std::sqrt(1 / <a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a>) * projected_value;</div>
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<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span> }</div>
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<div class="line"><a id="l00722" name="l00722"></a><span class="lineno"> 722</span> });</div>
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<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"> 723</span> <span class="keyword">const</span> <span class="keywordtype">double</span> final_objective_value =</div>
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<div class="line"><a id="l00724" name="l00724"></a><span class="lineno"> 724</span> sharder.ParallelSumOverShards([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00725" name="l00725"></a><span class="lineno"> 725</span> <span class="keywordtype">double</span> local_sum = 0.0;</div>
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<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"> 726</span> <span class="keyword">const</span> int64_t shard_start = sharder.ShardStart(shard.Index());</div>
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<div class="line"><a id="l00727" name="l00727"></a><span class="lineno"> 727</span> <span class="keywordflow">for</span> (int64_t i = shard_start;</div>
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<div class="line"><a id="l00728" name="l00728"></a><span class="lineno"> 728</span> i < shard_start + sharder.ShardSize(shard.Index()); ++i) {</div>
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<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"> 729</span> <span class="keyword">const</span> <span class="keywordtype">double</span> diff = solution[i] - problem.CenterPoint(i);</div>
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<div class="line"><a id="l00730" name="l00730"></a><span class="lineno"> 730</span> local_sum +=</div>
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<div class="line"><a id="l00731" name="l00731"></a><span class="lineno"> 731</span> 0.5 * diff * problem.ObjectiveMatrixDiagonalAt(i) * diff +</div>
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<div class="line"><a id="l00732" name="l00732"></a><span class="lineno"> 732</span> diff * problem.Objective(i);</div>
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<div class="line"><a id="l00733" name="l00733"></a><span class="lineno"> 733</span> }</div>
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<div class="line"><a id="l00734" name="l00734"></a><span class="lineno"> 734</span> <span class="keywordflow">return</span> local_sum;</div>
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<div class="line"><a id="l00735" name="l00735"></a><span class="lineno"> 735</span> });</div>
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<div class="line"><a id="l00736" name="l00736"></a><span class="lineno"> 736</span> <span class="keywordflow">return</span> {.solution_step_size = optimal_scaling,</div>
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<div class="line"><a id="l00737" name="l00737"></a><span class="lineno"> 737</span> .objective_value = final_objective_value,</div>
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<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"> 738</span> .solution = solution};</div>
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<div class="line"><a id="l00739" name="l00739"></a><span class="lineno"> 739</span>}</div>
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<div class="line"><a id="l00740" name="l00740"></a><span class="lineno"> 740</span> </div>
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<div class="line"><a id="l00741" name="l00741"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a5f128477eac14f0eda4b73fdfb3e24d4"> 741</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html">TrustRegionResult</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a5f128477eac14f0eda4b73fdfb3e24d4">SolveDiagonalTrustRegion</a>(</div>
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<div class="line"><a id="l00742" name="l00742"></a><span class="lineno"> 742</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#ac824522e23b1d307c272d07493af3a65">objective_vector</a>, <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#ad8dc72e7835d167fffffac5769c55076">objective_matrix_diagonal</a>,</div>
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<div class="line"><a id="l00743" name="l00743"></a><span class="lineno"> 743</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#a16346c4c462dec8f0cf38493c5e0358c">variable_lower_bounds</a>,</div>
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<div class="line"><a id="l00744" name="l00744"></a><span class="lineno"> 744</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#a868af74445e29f368ccf4a9e053f9267">variable_upper_bounds</a>, <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>,</div>
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<div class="line"><a id="l00745" name="l00745"></a><span class="lineno"> 745</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#ad31783425c63eac33cc6aade41a6537d">norm_weights</a>, <span class="keyword">const</span> <span class="keywordtype">double</span> target_radius,</div>
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<div class="line"><a id="l00746" name="l00746"></a><span class="lineno"> 746</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a>& sharder, <span class="keyword">const</span> <span class="keywordtype">double</span> solve_tolerance) {</div>
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<div class="line"><a id="l00747" name="l00747"></a><span class="lineno"> 747</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html">DiagonalTrustRegionProblem</a> problem(</div>
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<div class="line"><a id="l00748" name="l00748"></a><span class="lineno"> 748</span> &<a class="code hl_variable" href="trust__region__test_8cc.html#ac824522e23b1d307c272d07493af3a65">objective_vector</a>, &<a class="code hl_variable" href="trust__region__test_8cc.html#ad8dc72e7835d167fffffac5769c55076">objective_matrix_diagonal</a>, &<a class="code hl_variable" href="trust__region__test_8cc.html#a16346c4c462dec8f0cf38493c5e0358c">variable_lower_bounds</a>,</div>
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<div class="line"><a id="l00749" name="l00749"></a><span class="lineno"> 749</span> &<a class="code hl_variable" href="trust__region__test_8cc.html#a868af74445e29f368ccf4a9e053f9267">variable_upper_bounds</a>, &<a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>, &<a class="code hl_variable" href="trust__region__test_8cc.html#ad31783425c63eac33cc6aade41a6537d">norm_weights</a>);</div>
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<div class="line"><a id="l00750" name="l00750"></a><span class="lineno"> 750</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a39db3ccea12adec49816af128a288223">SolveDiagonalTrustRegionProblem</a>(problem, sharder, target_radius,</div>
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<div class="line"><a id="l00751" name="l00751"></a><span class="lineno"> 751</span> solve_tolerance);</div>
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<div class="line"><a id="l00752" name="l00752"></a><span class="lineno"> 752</span>}</div>
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<div class="line"><a id="l00753" name="l00753"></a><span class="lineno"> 753</span> </div>
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<div class="line"><a id="l00754" name="l00754"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a64c21ba4bf7d15e5dd1f8396074a9dfa"> 754</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html">TrustRegionResult</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a64c21ba4bf7d15e5dd1f8396074a9dfa">SolveDiagonalQpTrustRegion</a>(</div>
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<div class="line"><a id="l00755" name="l00755"></a><span class="lineno"> 755</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp, <span class="keyword">const</span> VectorXd& primal_solution,</div>
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<div class="line"><a id="l00756" name="l00756"></a><span class="lineno"> 756</span> <span class="keyword">const</span> VectorXd& dual_solution, <span class="keyword">const</span> VectorXd& primal_gradient,</div>
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<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"> 757</span> <span class="keyword">const</span> VectorXd& dual_gradient, <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight,</div>
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<div class="line"><a id="l00758" name="l00758"></a><span class="lineno"> 758</span> <span class="keywordtype">double</span> target_radius, <span class="keyword">const</span> <span class="keywordtype">double</span> solve_tolerance) {</div>
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<div class="line"><a id="l00759" name="l00759"></a><span class="lineno"> 759</span> <span class="keyword">const</span> int64_t problem_size = sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab945b88f1937277a896d4c7c7935d605">PrimalSize</a>() + sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#afcafa95b1a351212291c7a030deec52a">DualSize</a>();</div>
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<div class="line"><a id="l00760" name="l00760"></a><span class="lineno"> 760</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html">DiagonalTrustRegionProblemFromQp</a> problem(&sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>(), &primal_solution,</div>
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<div class="line"><a id="l00761" name="l00761"></a><span class="lineno"> 761</span> &dual_solution, &primal_gradient,</div>
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<div class="line"><a id="l00762" name="l00762"></a><span class="lineno"> 762</span> &dual_gradient, primal_weight);</div>
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<div class="line"><a id="l00763" name="l00763"></a><span class="lineno"> 763</span> </div>
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<div class="line"><a id="l00764" name="l00764"></a><span class="lineno"> 764</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a> joint_sharder(sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>(), problem_size);</div>
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<div class="line"><a id="l00765" name="l00765"></a><span class="lineno"> 765</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> norm_weights_are_positive =</div>
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<div class="line"><a id="l00766" name="l00766"></a><span class="lineno"> 766</span> joint_sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a9761cf0a21e5b7efe9126765eec48a3a">ParallelTrueForAllShards</a>([&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00767" name="l00767"></a><span class="lineno"> 767</span> <span class="keyword">const</span> int64_t shard_start = joint_sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#abfb02437c97584ca43c040284aecf748">ShardStart</a>(shard.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">Index</a>());</div>
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<div class="line"><a id="l00768" name="l00768"></a><span class="lineno"> 768</span> for (int64_t i = shard_start;</div>
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<div class="line"><a id="l00769" name="l00769"></a><span class="lineno"> 769</span> i < shard_start + joint_sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a998aef9096f234a37e58caddca6db203">ShardSize</a>(shard.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">Index</a>()); ++i) {</div>
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<div class="line"><a id="l00770" name="l00770"></a><span class="lineno"> 770</span> if (problem.NormWeight(i) <= 0) {</div>
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<div class="line"><a id="l00771" name="l00771"></a><span class="lineno"> 771</span> return false;</div>
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<div class="line"><a id="l00772" name="l00772"></a><span class="lineno"> 772</span> }</div>
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<div class="line"><a id="l00773" name="l00773"></a><span class="lineno"> 773</span> }</div>
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<div class="line"><a id="l00774" name="l00774"></a><span class="lineno"> 774</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00775" name="l00775"></a><span class="lineno"> 775</span> });</div>
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<div class="line"><a id="l00776" name="l00776"></a><span class="lineno"> 776</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(norm_weights_are_positive);</div>
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<div class="line"><a id="l00777" name="l00777"></a><span class="lineno"> 777</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a39db3ccea12adec49816af128a288223">SolveDiagonalTrustRegionProblem</a>(problem, joint_sharder, target_radius,</div>
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<div class="line"><a id="l00778" name="l00778"></a><span class="lineno"> 778</span> solve_tolerance);</div>
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<div class="line"><a id="l00779" name="l00779"></a><span class="lineno"> 779</span>}</div>
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<div class="line"><a id="l00780" name="l00780"></a><span class="lineno"> 780</span> </div>
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<div class="line"><a id="l00781" name="l00781"></a><span class="lineno"> 781</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00782" name="l00782"></a><span class="lineno"> 782</span> </div>
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<div class="line"><a id="l00783" name="l00783"></a><span class="lineno"> 783</span><span class="keyword">struct </span>MaxNormBoundResult {</div>
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<div class="line"><a id="l00784" name="l00784"></a><span class="lineno"> 784</span> <span class="comment">// LagrangianPart.value from ComputePrimalGradient and ComputeDualGradient,</span></div>
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<div class="line"><a id="l00785" name="l00785"></a><span class="lineno"> 785</span> <span class="comment">// respectively.</span></div>
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<div class="line"><a id="l00786" name="l00786"></a><span class="lineno"><a class="line" href="trust__region_8cc.html#a59572487cff4d7cb15cdabbffd9685b2"> 786</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="trust__region_8cc.html#a59572487cff4d7cb15cdabbffd9685b2">part_of_lagrangian_value</a> = 0.0;</div>
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<div class="line"><a id="l00787" name="l00787"></a><span class="lineno"> 787</span> <span class="comment">// For the primal, the value</span></div>
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<div class="line"><a id="l00788" name="l00788"></a><span class="lineno"> 788</span> <span class="comment">// ∇_x L(primal_solution, dual_solution)^T (x^* - primal_solution) where</span></div>
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<div class="line"><a id="l00789" name="l00789"></a><span class="lineno"> 789</span> <span class="comment">// x^* is the solution of the primal trust region subproblem.</span></div>
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<div class="line"><a id="l00790" name="l00790"></a><span class="lineno"> 790</span> <span class="comment">// For the dual, the value</span></div>
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<div class="line"><a id="l00791" name="l00791"></a><span class="lineno"> 791</span> <span class="comment">// ∇_y L(primal_solution, dual_solution)^T (y^* - dual_solution) where</span></div>
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<div class="line"><a id="l00792" name="l00792"></a><span class="lineno"> 792</span> <span class="comment">// y^* is the solution of the dual trust region subproblem.</span></div>
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<div class="line"><a id="l00793" name="l00793"></a><span class="lineno"> 793</span> <span class="comment">// This will be a non-positive value for the primal and a non-negative</span></div>
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<div class="line"><a id="l00794" name="l00794"></a><span class="lineno"> 794</span> <span class="comment">// value for the dual.</span></div>
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<div class="line"><a id="l00795" name="l00795"></a><span class="lineno"><a class="line" href="trust__region_8cc.html#a35a93e273ed07f347699c3f4b4b5f581"> 795</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="trust__region_8cc.html#a35a93e273ed07f347699c3f4b4b5f581">trust_region_objective_delta</a> = 0.0;</div>
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<div class="line"><a id="l00796" name="l00796"></a><span class="lineno"> 796</span>};</div>
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<div class="line"><a id="l00797" name="l00797"></a><span class="lineno"> 797</span> </div>
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<div class="line"><a id="l00798" name="l00798"></a><span class="lineno"> 798</span>MaxNormBoundResult ComputeMaxNormPrimalTrustRegionBound(</div>
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<div class="line"><a id="l00799" name="l00799"></a><span class="lineno"> 799</span> <span class="keyword">const</span> ShardedQuadraticProgram& sharded_qp, <span class="keyword">const</span> VectorXd& primal_solution,</div>
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<div class="line"><a id="l00800" name="l00800"></a><span class="lineno"> 800</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_radius, <span class="keyword">const</span> VectorXd& dual_product) {</div>
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<div class="line"><a id="l00801" name="l00801"></a><span class="lineno"> 801</span> LagrangianPart primal_part =</div>
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<div class="line"><a id="l00802" name="l00802"></a><span class="lineno"> 802</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a259d3f73717a2ababa9df2dd43914656">ComputePrimalGradient</a>(sharded_qp, primal_solution, dual_product);</div>
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<div class="line"><a id="l00803" name="l00803"></a><span class="lineno"> 803</span> internal::PrimalTrustRegionProblem primal_problem(</div>
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<div class="line"><a id="l00804" name="l00804"></a><span class="lineno"> 804</span> &sharded_qp.Qp(), &primal_solution, &primal_part.gradient);</div>
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<div class="line"><a id="l00805" name="l00805"></a><span class="lineno"> 805</span> TrustRegionResultStepSize trust_region_result = SolveTrustRegionStepSize(</div>
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<div class="line"><a id="l00806" name="l00806"></a><span class="lineno"> 806</span> primal_problem, primal_radius, sharded_qp.PrimalSharder());</div>
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|
<div class="line"><a id="l00807" name="l00807"></a><span class="lineno"> 807</span> <span class="keywordflow">return</span> {.part_of_lagrangian_value = primal_part.value,</div>
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|
<div class="line"><a id="l00808" name="l00808"></a><span class="lineno"> 808</span> .trust_region_objective_delta = trust_region_result.objective_value};</div>
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|
<div class="line"><a id="l00809" name="l00809"></a><span class="lineno"> 809</span>}</div>
|
|
<div class="line"><a id="l00810" name="l00810"></a><span class="lineno"> 810</span> </div>
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<div class="line"><a id="l00811" name="l00811"></a><span class="lineno"> 811</span>MaxNormBoundResult ComputeMaxNormDualTrustRegionBound(</div>
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|
<div class="line"><a id="l00812" name="l00812"></a><span class="lineno"> 812</span> <span class="keyword">const</span> ShardedQuadraticProgram& sharded_qp, <span class="keyword">const</span> VectorXd& dual_solution,</div>
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<div class="line"><a id="l00813" name="l00813"></a><span class="lineno"> 813</span> <span class="keyword">const</span> <span class="keywordtype">double</span> dual_radius, <span class="keyword">const</span> VectorXd& primal_product) {</div>
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|
<div class="line"><a id="l00814" name="l00814"></a><span class="lineno"> 814</span> LagrangianPart dual_part =</div>
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|
<div class="line"><a id="l00815" name="l00815"></a><span class="lineno"> 815</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a608ed26a4c7ff3bdcb22d25ff890f47d">ComputeDualGradient</a>(sharded_qp, dual_solution, primal_product);</div>
|
|
<div class="line"><a id="l00816" name="l00816"></a><span class="lineno"> 816</span> internal::DualTrustRegionProblem dual_problem(</div>
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|
<div class="line"><a id="l00817" name="l00817"></a><span class="lineno"> 817</span> &sharded_qp.Qp(), &dual_solution, &dual_part.gradient);</div>
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|
<div class="line"><a id="l00818" name="l00818"></a><span class="lineno"> 818</span> TrustRegionResultStepSize trust_region_result = SolveTrustRegionStepSize(</div>
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|
<div class="line"><a id="l00819" name="l00819"></a><span class="lineno"> 819</span> dual_problem, dual_radius, sharded_qp.DualSharder());</div>
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|
<div class="line"><a id="l00820" name="l00820"></a><span class="lineno"> 820</span> <span class="keywordflow">return</span> {.part_of_lagrangian_value = dual_part.value,</div>
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|
<div class="line"><a id="l00821" name="l00821"></a><span class="lineno"> 821</span> .trust_region_objective_delta = -trust_region_result.objective_value};</div>
|
|
<div class="line"><a id="l00822" name="l00822"></a><span class="lineno"> 822</span>}</div>
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|
<div class="line"><a id="l00823" name="l00823"></a><span class="lineno"> 823</span> </div>
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|
<div class="line"><a id="l00824" name="l00824"></a><span class="lineno"> 824</span><span class="comment">// Returns the largest radius that the primal could move (in Euclidean distance)</span></div>
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|
<div class="line"><a id="l00825" name="l00825"></a><span class="lineno"> 825</span><span class="comment">// to match the weighted_distance. This is the largest value of ||x||_2 such</span></div>
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|
<div class="line"><a id="l00826" name="l00826"></a><span class="lineno"> 826</span><span class="comment">// that there exists a y such that max{||x||_P, ||y||_D} <= weighted_distance.</span></div>
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|
<div class="line"><a id="l00827" name="l00827"></a><span class="lineno"> 827</span><span class="keywordtype">double</span> MaximumPrimalDistanceGivenWeightedDistance(</div>
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|
<div class="line"><a id="l00828" name="l00828"></a><span class="lineno"> 828</span> <span class="keyword">const</span> <span class="keywordtype">double</span> weighted_distance, <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight) {</div>
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|
<div class="line"><a id="l00829" name="l00829"></a><span class="lineno"> 829</span> <span class="keywordflow">return</span> std::sqrt(2) * weighted_distance / std::sqrt(primal_weight);</div>
|
|
<div class="line"><a id="l00830" name="l00830"></a><span class="lineno"> 830</span>}</div>
|
|
<div class="line"><a id="l00831" name="l00831"></a><span class="lineno"> 831</span> </div>
|
|
<div class="line"><a id="l00832" name="l00832"></a><span class="lineno"> 832</span><span class="comment">// Returns the largest radius that the dual could move (in Euclidean distance)</span></div>
|
|
<div class="line"><a id="l00833" name="l00833"></a><span class="lineno"> 833</span><span class="comment">// to match the weighted_distance. This is the largest value of ||y||_2 such</span></div>
|
|
<div class="line"><a id="l00834" name="l00834"></a><span class="lineno"> 834</span><span class="comment">// that there exists an x such that max{||x||_P, ||y||_D} <= weighted_distance.</span></div>
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|
<div class="line"><a id="l00835" name="l00835"></a><span class="lineno"> 835</span><span class="keywordtype">double</span> MaximumDualDistanceGivenWeightedDistance(<span class="keyword">const</span> <span class="keywordtype">double</span> weighted_distance,</div>
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|
<div class="line"><a id="l00836" name="l00836"></a><span class="lineno"> 836</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight) {</div>
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|
<div class="line"><a id="l00837" name="l00837"></a><span class="lineno"> 837</span> <span class="keywordflow">return</span> std::sqrt(2) * weighted_distance * std::sqrt(primal_weight);</div>
|
|
<div class="line"><a id="l00838" name="l00838"></a><span class="lineno"> 838</span>}</div>
|
|
<div class="line"><a id="l00839" name="l00839"></a><span class="lineno"> 839</span> </div>
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|
<div class="line"><a id="l00840" name="l00840"></a><span class="lineno"> 840</span>LocalizedLagrangianBounds ComputeMaxNormLocalizedLagrangianBounds(</div>
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|
<div class="line"><a id="l00841" name="l00841"></a><span class="lineno"> 841</span> <span class="keyword">const</span> ShardedQuadraticProgram& sharded_qp, <span class="keyword">const</span> VectorXd& primal_solution,</div>
|
|
<div class="line"><a id="l00842" name="l00842"></a><span class="lineno"> 842</span> <span class="keyword">const</span> VectorXd& dual_solution, <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight,</div>
|
|
<div class="line"><a id="l00843" name="l00843"></a><span class="lineno"> 843</span> <span class="keyword">const</span> <span class="keywordtype">double</span> radius, <span class="keyword">const</span> Eigen::VectorXd& primal_product,</div>
|
|
<div class="line"><a id="l00844" name="l00844"></a><span class="lineno"> 844</span> <span class="keyword">const</span> Eigen::VectorXd& dual_product) {</div>
|
|
<div class="line"><a id="l00845" name="l00845"></a><span class="lineno"> 845</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_radius =</div>
|
|
<div class="line"><a id="l00846" name="l00846"></a><span class="lineno"> 846</span> MaximumPrimalDistanceGivenWeightedDistance(radius, primal_weight);</div>
|
|
<div class="line"><a id="l00847" name="l00847"></a><span class="lineno"> 847</span> <span class="keyword">const</span> <span class="keywordtype">double</span> dual_radius =</div>
|
|
<div class="line"><a id="l00848" name="l00848"></a><span class="lineno"> 848</span> MaximumDualDistanceGivenWeightedDistance(radius, primal_weight);</div>
|
|
<div class="line"><a id="l00849" name="l00849"></a><span class="lineno"> 849</span> </div>
|
|
<div class="line"><a id="l00850" name="l00850"></a><span class="lineno"> 850</span> <span class="comment">// The max norm means that the optimization over the primal and the dual can</span></div>
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|
<div class="line"><a id="l00851" name="l00851"></a><span class="lineno"> 851</span> <span class="comment">// be done independently.</span></div>
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|
<div class="line"><a id="l00852" name="l00852"></a><span class="lineno"> 852</span> </div>
|
|
<div class="line"><a id="l00853" name="l00853"></a><span class="lineno"> 853</span> MaxNormBoundResult primal_result = ComputeMaxNormPrimalTrustRegionBound(</div>
|
|
<div class="line"><a id="l00854" name="l00854"></a><span class="lineno"> 854</span> sharded_qp, primal_solution, primal_radius, dual_product);</div>
|
|
<div class="line"><a id="l00855" name="l00855"></a><span class="lineno"> 855</span> </div>
|
|
<div class="line"><a id="l00856" name="l00856"></a><span class="lineno"> 856</span> MaxNormBoundResult dual_result = ComputeMaxNormDualTrustRegionBound(</div>
|
|
<div class="line"><a id="l00857" name="l00857"></a><span class="lineno"> 857</span> sharded_qp, dual_solution, dual_radius, primal_product);</div>
|
|
<div class="line"><a id="l00858" name="l00858"></a><span class="lineno"> 858</span> </div>
|
|
<div class="line"><a id="l00859" name="l00859"></a><span class="lineno"> 859</span> <span class="keyword">const</span> <span class="keywordtype">double</span> lagrangian_value = primal_result.part_of_lagrangian_value +</div>
|
|
<div class="line"><a id="l00860" name="l00860"></a><span class="lineno"> 860</span> dual_result.part_of_lagrangian_value;</div>
|
|
<div class="line"><a id="l00861" name="l00861"></a><span class="lineno"> 861</span> </div>
|
|
<div class="line"><a id="l00862" name="l00862"></a><span class="lineno"> 862</span> <span class="keywordflow">return</span> LocalizedLagrangianBounds{</div>
|
|
<div class="line"><a id="l00863" name="l00863"></a><span class="lineno"> 863</span> .lagrangian_value = lagrangian_value,</div>
|
|
<div class="line"><a id="l00864" name="l00864"></a><span class="lineno"> 864</span> .lower_bound =</div>
|
|
<div class="line"><a id="l00865" name="l00865"></a><span class="lineno"> 865</span> lagrangian_value + primal_result.trust_region_objective_delta,</div>
|
|
<div class="line"><a id="l00866" name="l00866"></a><span class="lineno"> 866</span> .upper_bound =</div>
|
|
<div class="line"><a id="l00867" name="l00867"></a><span class="lineno"> 867</span> lagrangian_value + dual_result.trust_region_objective_delta,</div>
|
|
<div class="line"><a id="l00868" name="l00868"></a><span class="lineno"> 868</span> .radius = radius};</div>
|
|
<div class="line"><a id="l00869" name="l00869"></a><span class="lineno"> 869</span>}</div>
|
|
<div class="line"><a id="l00870" name="l00870"></a><span class="lineno"> 870</span> </div>
|
|
<div class="line"><a id="l00871" name="l00871"></a><span class="lineno"> 871</span>LocalizedLagrangianBounds ComputeEuclideanNormLocalizedLagrangianBounds(</div>
|
|
<div class="line"><a id="l00872" name="l00872"></a><span class="lineno"> 872</span> <span class="keyword">const</span> ShardedQuadraticProgram& sharded_qp, <span class="keyword">const</span> VectorXd& primal_solution,</div>
|
|
<div class="line"><a id="l00873" name="l00873"></a><span class="lineno"> 873</span> <span class="keyword">const</span> VectorXd& dual_solution, <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight,</div>
|
|
<div class="line"><a id="l00874" name="l00874"></a><span class="lineno"> 874</span> <span class="keyword">const</span> <span class="keywordtype">double</span> radius, <span class="keyword">const</span> Eigen::VectorXd& primal_product,</div>
|
|
<div class="line"><a id="l00875" name="l00875"></a><span class="lineno"> 875</span> <span class="keyword">const</span> Eigen::VectorXd& dual_product,</div>
|
|
<div class="line"><a id="l00876" name="l00876"></a><span class="lineno"> 876</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> use_diagonal_qp_trust_region_solver,</div>
|
|
<div class="line"><a id="l00877" name="l00877"></a><span class="lineno"> 877</span> <span class="keyword">const</span> <span class="keywordtype">double</span> diagonal_qp_trust_region_solver_tolerance) {</div>
|
|
<div class="line"><a id="l00878" name="l00878"></a><span class="lineno"> 878</span> <span class="keyword">const</span> QuadraticProgram& qp = sharded_qp.Qp();</div>
|
|
<div class="line"><a id="l00879" name="l00879"></a><span class="lineno"> 879</span> <span class="keyword">const</span> LagrangianPart primal_part =</div>
|
|
<div class="line"><a id="l00880" name="l00880"></a><span class="lineno"> 880</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a259d3f73717a2ababa9df2dd43914656">ComputePrimalGradient</a>(sharded_qp, primal_solution, dual_product);</div>
|
|
<div class="line"><a id="l00881" name="l00881"></a><span class="lineno"> 881</span> <span class="keyword">const</span> LagrangianPart dual_part =</div>
|
|
<div class="line"><a id="l00882" name="l00882"></a><span class="lineno"> 882</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a608ed26a4c7ff3bdcb22d25ff890f47d">ComputeDualGradient</a>(sharded_qp, dual_solution, primal_product);</div>
|
|
<div class="line"><a id="l00883" name="l00883"></a><span class="lineno"> 883</span> </div>
|
|
<div class="line"><a id="l00884" name="l00884"></a><span class="lineno"> 884</span> VectorXd trust_region_solution;</div>
|
|
<div class="line"><a id="l00885" name="l00885"></a><span class="lineno"> 885</span> <span class="keyword">const</span> <span class="keywordtype">double</span> lagrangian_value = primal_part.value + dual_part.value;</div>
|
|
<div class="line"><a id="l00886" name="l00886"></a><span class="lineno"> 886</span> </div>
|
|
<div class="line"><a id="l00887" name="l00887"></a><span class="lineno"> 887</span> Sharder joint_sharder(</div>
|
|
<div class="line"><a id="l00888" name="l00888"></a><span class="lineno"> 888</span> sharded_qp.PrimalSharder(),</div>
|
|
<div class="line"><a id="l00889" name="l00889"></a><span class="lineno"> 889</span> <span class="comment">/*num_elements=*/</span>sharded_qp.PrimalSize() + sharded_qp.DualSize());</div>
|
|
<div class="line"><a id="l00890" name="l00890"></a><span class="lineno"> 890</span> </div>
|
|
<div class="line"><a id="l00891" name="l00891"></a><span class="lineno"> 891</span> <span class="keywordflow">if</span> (use_diagonal_qp_trust_region_solver) {</div>
|
|
<div class="line"><a id="l00892" name="l00892"></a><span class="lineno"> 892</span> DiagonalTrustRegionProblemFromQp problem(</div>
|
|
<div class="line"><a id="l00893" name="l00893"></a><span class="lineno"> 893</span> &qp, &primal_solution, &dual_solution, &primal_part.gradient,</div>
|
|
<div class="line"><a id="l00894" name="l00894"></a><span class="lineno"> 894</span> &dual_part.gradient, primal_weight);</div>
|
|
<div class="line"><a id="l00895" name="l00895"></a><span class="lineno"> 895</span> </div>
|
|
<div class="line"><a id="l00896" name="l00896"></a><span class="lineno"> 896</span> trust_region_solution = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a39db3ccea12adec49816af128a288223">SolveDiagonalTrustRegionProblem</a>(</div>
|
|
<div class="line"><a id="l00897" name="l00897"></a><span class="lineno"> 897</span> problem, joint_sharder, radius,</div>
|
|
<div class="line"><a id="l00898" name="l00898"></a><span class="lineno"> 898</span> diagonal_qp_trust_region_solver_tolerance)</div>
|
|
<div class="line"><a id="l00899" name="l00899"></a><span class="lineno"> 899</span> .<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a92098f9990f978c61c5dcb88815f008e">solution</a>;</div>
|
|
<div class="line"><a id="l00900" name="l00900"></a><span class="lineno"> 900</span> } <span class="keywordflow">else</span> {</div>
|
|
<div class="line"><a id="l00901" name="l00901"></a><span class="lineno"> 901</span> JointTrustRegionProblem joint_problem(&qp, &primal_solution, &dual_solution,</div>
|
|
<div class="line"><a id="l00902" name="l00902"></a><span class="lineno"> 902</span> &primal_part.gradient,</div>
|
|
<div class="line"><a id="l00903" name="l00903"></a><span class="lineno"> 903</span> &dual_part.gradient, primal_weight);</div>
|
|
<div class="line"><a id="l00904" name="l00904"></a><span class="lineno"> 904</span> </div>
|
|
<div class="line"><a id="l00905" name="l00905"></a><span class="lineno"> 905</span> TrustRegionResultStepSize trust_region_result =</div>
|
|
<div class="line"><a id="l00906" name="l00906"></a><span class="lineno"> 906</span> SolveTrustRegionStepSize(joint_problem, radius, joint_sharder);</div>
|
|
<div class="line"><a id="l00907" name="l00907"></a><span class="lineno"> 907</span> </div>
|
|
<div class="line"><a id="l00908" name="l00908"></a><span class="lineno"> 908</span> trust_region_solution = ComputeSolution(</div>
|
|
<div class="line"><a id="l00909" name="l00909"></a><span class="lineno"> 909</span> joint_problem, trust_region_result.solution_step_size, joint_sharder);</div>
|
|
<div class="line"><a id="l00910" name="l00910"></a><span class="lineno"> 910</span> }</div>
|
|
<div class="line"><a id="l00911" name="l00911"></a><span class="lineno"> 911</span> </div>
|
|
<div class="line"><a id="l00912" name="l00912"></a><span class="lineno"> 912</span> <span class="keyword">auto</span> primal_trust_region_solution =</div>
|
|
<div class="line"><a id="l00913" name="l00913"></a><span class="lineno"> 913</span> trust_region_solution.segment(0, sharded_qp.PrimalSize());</div>
|
|
<div class="line"><a id="l00914" name="l00914"></a><span class="lineno"> 914</span> <span class="keyword">auto</span> dual_trust_region_solution = trust_region_solution.segment(</div>
|
|
<div class="line"><a id="l00915" name="l00915"></a><span class="lineno"> 915</span> sharded_qp.PrimalSize(), sharded_qp.DualSize());</div>
|
|
<div class="line"><a id="l00916" name="l00916"></a><span class="lineno"> 916</span> </div>
|
|
<div class="line"><a id="l00917" name="l00917"></a><span class="lineno"> 917</span> <span class="comment">// ∇_x L(primal_solution, dual_solution)^T (x - primal_solution)</span></div>
|
|
<div class="line"><a id="l00918" name="l00918"></a><span class="lineno"> 918</span> <span class="keywordtype">double</span> primal_objective_delta =</div>
|
|
<div class="line"><a id="l00919" name="l00919"></a><span class="lineno"> 919</span> sharded_qp.PrimalSharder().ParallelSumOverShards(</div>
|
|
<div class="line"><a id="l00920" name="l00920"></a><span class="lineno"> 920</span> [&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
|
|
<div class="line"><a id="l00921" name="l00921"></a><span class="lineno"> 921</span> <span class="keywordflow">return</span> shard(primal_part.gradient)</div>
|
|
<div class="line"><a id="l00922" name="l00922"></a><span class="lineno"> 922</span> .dot(shard(primal_trust_region_solution) -</div>
|
|
<div class="line"><a id="l00923" name="l00923"></a><span class="lineno"> 923</span> shard(primal_solution));</div>
|
|
<div class="line"><a id="l00924" name="l00924"></a><span class="lineno"> 924</span> });</div>
|
|
<div class="line"><a id="l00925" name="l00925"></a><span class="lineno"> 925</span> </div>
|
|
<div class="line"><a id="l00926" name="l00926"></a><span class="lineno"> 926</span> <span class="comment">// Take into account the quadratic's contribution if the diagonal QP solver</span></div>
|
|
<div class="line"><a id="l00927" name="l00927"></a><span class="lineno"> 927</span> <span class="comment">// is enabled.</span></div>
|
|
<div class="line"><a id="l00928" name="l00928"></a><span class="lineno"> 928</span> <span class="keywordflow">if</span> (use_diagonal_qp_trust_region_solver &&</div>
|
|
<div class="line"><a id="l00929" name="l00929"></a><span class="lineno"> 929</span> sharded_qp.Qp().objective_matrix.has_value()) {</div>
|
|
<div class="line"><a id="l00930" name="l00930"></a><span class="lineno"> 930</span> primal_objective_delta += sharded_qp.PrimalSharder().ParallelSumOverShards(</div>
|
|
<div class="line"><a id="l00931" name="l00931"></a><span class="lineno"> 931</span> [&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
|
|
<div class="line"><a id="l00932" name="l00932"></a><span class="lineno"> 932</span> <span class="keyword">const</span> <span class="keywordtype">int</span> shard_start =</div>
|
|
<div class="line"><a id="l00933" name="l00933"></a><span class="lineno"> 933</span> sharded_qp.PrimalSharder().ShardStart(shard.Index());</div>
|
|
<div class="line"><a id="l00934" name="l00934"></a><span class="lineno"> 934</span> <span class="keyword">const</span> <span class="keywordtype">int</span> shard_size =</div>
|
|
<div class="line"><a id="l00935" name="l00935"></a><span class="lineno"> 935</span> sharded_qp.PrimalSharder().ShardSize(shard.Index());</div>
|
|
<div class="line"><a id="l00936" name="l00936"></a><span class="lineno"> 936</span> <span class="keywordtype">double</span> sum = 0.0;</div>
|
|
<div class="line"><a id="l00937" name="l00937"></a><span class="lineno"> 937</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = shard_start; i < shard_start + shard_size; ++i) {</div>
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<div class="line"><a id="l00938" name="l00938"></a><span class="lineno"> 938</span> sum += 0.5 * sharded_qp.Qp().objective_matrix->diagonal()[i] *</div>
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<div class="line"><a id="l00939" name="l00939"></a><span class="lineno"> 939</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">MathUtil::Square</a>(primal_trust_region_solution[i] -</div>
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<div class="line"><a id="l00940" name="l00940"></a><span class="lineno"> 940</span> primal_solution[i]);</div>
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<div class="line"><a id="l00941" name="l00941"></a><span class="lineno"> 941</span> }</div>
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<div class="line"><a id="l00942" name="l00942"></a><span class="lineno"> 942</span> <span class="keywordflow">return</span> sum;</div>
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<div class="line"><a id="l00943" name="l00943"></a><span class="lineno"> 943</span> });</div>
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<div class="line"><a id="l00944" name="l00944"></a><span class="lineno"> 944</span> }</div>
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<div class="line"><a id="l00945" name="l00945"></a><span class="lineno"> 945</span> </div>
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<div class="line"><a id="l00946" name="l00946"></a><span class="lineno"> 946</span> <span class="comment">// ∇_y L(primal_solution, dual_solution)^T (y - dual_solution)</span></div>
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<div class="line"><a id="l00947" name="l00947"></a><span class="lineno"> 947</span> <span class="keyword">const</span> <span class="keywordtype">double</span> dual_objective_delta =</div>
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<div class="line"><a id="l00948" name="l00948"></a><span class="lineno"> 948</span> sharded_qp.DualSharder().ParallelSumOverShards(</div>
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<div class="line"><a id="l00949" name="l00949"></a><span class="lineno"> 949</span> [&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00950" name="l00950"></a><span class="lineno"> 950</span> <span class="keywordflow">return</span> shard(dual_part.gradient)</div>
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<div class="line"><a id="l00951" name="l00951"></a><span class="lineno"> 951</span> .dot(shard(dual_trust_region_solution) - shard(dual_solution));</div>
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<div class="line"><a id="l00952" name="l00952"></a><span class="lineno"> 952</span> });</div>
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<div class="line"><a id="l00953" name="l00953"></a><span class="lineno"> 953</span> </div>
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<div class="line"><a id="l00954" name="l00954"></a><span class="lineno"> 954</span> <span class="keywordflow">return</span> LocalizedLagrangianBounds{</div>
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<div class="line"><a id="l00955" name="l00955"></a><span class="lineno"> 955</span> .lagrangian_value = lagrangian_value,</div>
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<div class="line"><a id="l00956" name="l00956"></a><span class="lineno"> 956</span> .lower_bound = lagrangian_value + primal_objective_delta,</div>
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<div class="line"><a id="l00957" name="l00957"></a><span class="lineno"> 957</span> .upper_bound = lagrangian_value + dual_objective_delta,</div>
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<div class="line"><a id="l00958" name="l00958"></a><span class="lineno"> 958</span> .radius = radius};</div>
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<div class="line"><a id="l00959" name="l00959"></a><span class="lineno"> 959</span>}</div>
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<div class="line"><a id="l00960" name="l00960"></a><span class="lineno"> 960</span> </div>
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<div class="line"><a id="l00961" name="l00961"></a><span class="lineno"> 961</span>} <span class="comment">// namespace</span></div>
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<div class="line"><a id="l00962" name="l00962"></a><span class="lineno"> 962</span> </div>
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<div class="line"><a id="l00963" name="l00963"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#adb77e7cede2fecf6bccfa93226b49c0b"> 963</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html">LocalizedLagrangianBounds</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#adb77e7cede2fecf6bccfa93226b49c0b">ComputeLocalizedLagrangianBounds</a>(</div>
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<div class="line"><a id="l00964" name="l00964"></a><span class="lineno"> 964</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp, <span class="keyword">const</span> VectorXd& primal_solution,</div>
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<div class="line"><a id="l00965" name="l00965"></a><span class="lineno"> 965</span> <span class="keyword">const</span> VectorXd& dual_solution, <span class="keyword">const</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1pdlp.html#a39f9a12aa1bd94ddb3a56816d4d25eb0">PrimalDualNorm</a> primal_dual_norm,</div>
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<div class="line"><a id="l00966" name="l00966"></a><span class="lineno"> 966</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_weight, <span class="keyword">const</span> <span class="keywordtype">double</span> radius,</div>
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<div class="line"><a id="l00967" name="l00967"></a><span class="lineno"> 967</span> <span class="keyword">const</span> VectorXd* primal_product, <span class="keyword">const</span> VectorXd* dual_product,</div>
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<div class="line"><a id="l00968" name="l00968"></a><span class="lineno"> 968</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> use_diagonal_qp_trust_region_solver,</div>
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<div class="line"><a id="l00969" name="l00969"></a><span class="lineno"> 969</span> <span class="keyword">const</span> <span class="keywordtype">double</span> diagonal_qp_trust_region_solver_tolerance) {</div>
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<div class="line"><a id="l00970" name="l00970"></a><span class="lineno"> 970</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a>& qp = sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>();</div>
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<div class="line"><a id="l00971" name="l00971"></a><span class="lineno"> 971</span> VectorXd primal_product_storage;</div>
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<div class="line"><a id="l00972" name="l00972"></a><span class="lineno"> 972</span> VectorXd dual_product_storage;</div>
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<div class="line"><a id="l00973" name="l00973"></a><span class="lineno"> 973</span> </div>
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<div class="line"><a id="l00974" name="l00974"></a><span class="lineno"> 974</span> <span class="keywordflow">if</span> (primal_product == <span class="keyword">nullptr</span>) {</div>
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<div class="line"><a id="l00975" name="l00975"></a><span class="lineno"> 975</span> primal_product_storage = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a463586ded0a114d3ca4b97a048d37d8a">TransposedMatrixVectorProduct</a>(</div>
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<div class="line"><a id="l00976" name="l00976"></a><span class="lineno"> 976</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a1e0d1154156a56084d0ba5232819b134">TransposedConstraintMatrix</a>(), primal_solution,</div>
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<div class="line"><a id="l00977" name="l00977"></a><span class="lineno"> 977</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a8bf92cdb63b602aba6f4d22b975e2f30">TransposedConstraintMatrixSharder</a>());</div>
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<div class="line"><a id="l00978" name="l00978"></a><span class="lineno"> 978</span> primal_product = &primal_product_storage;</div>
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<div class="line"><a id="l00979" name="l00979"></a><span class="lineno"> 979</span> }</div>
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<div class="line"><a id="l00980" name="l00980"></a><span class="lineno"> 980</span> <span class="keywordflow">if</span> (dual_product == <span class="keyword">nullptr</span>) {</div>
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<div class="line"><a id="l00981" name="l00981"></a><span class="lineno"> 981</span> dual_product_storage =</div>
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<div class="line"><a id="l00982" name="l00982"></a><span class="lineno"> 982</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a463586ded0a114d3ca4b97a048d37d8a">TransposedMatrixVectorProduct</a>(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae7a462ef3035095eff6c883ae0078d02">constraint_matrix</a>, dual_solution,</div>
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<div class="line"><a id="l00983" name="l00983"></a><span class="lineno"> 983</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ac9f7db642c1b4c4fc37f489f03d110a7">ConstraintMatrixSharder</a>());</div>
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<div class="line"><a id="l00984" name="l00984"></a><span class="lineno"> 984</span> dual_product = &dual_product_storage;</div>
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<div class="line"><a id="l00985" name="l00985"></a><span class="lineno"> 985</span> }</div>
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<div class="line"><a id="l00986" name="l00986"></a><span class="lineno"> 986</span> </div>
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<div class="line"><a id="l00987" name="l00987"></a><span class="lineno"> 987</span> <span class="keywordflow">switch</span> (primal_dual_norm) {</div>
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<div class="line"><a id="l00988" name="l00988"></a><span class="lineno"> 988</span> <span class="keywordflow">case</span> PrimalDualNorm::kMaxNorm:</div>
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<div class="line"><a id="l00989" name="l00989"></a><span class="lineno"> 989</span> <span class="keywordflow">return</span> ComputeMaxNormLocalizedLagrangianBounds(</div>
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<div class="line"><a id="l00990" name="l00990"></a><span class="lineno"> 990</span> sharded_qp, primal_solution, dual_solution, primal_weight, radius,</div>
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<div class="line"><a id="l00991" name="l00991"></a><span class="lineno"> 991</span> *primal_product, *dual_product);</div>
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<div class="line"><a id="l00992" name="l00992"></a><span class="lineno"> 992</span> <span class="keywordflow">case</span> PrimalDualNorm::kEuclideanNorm:</div>
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<div class="line"><a id="l00993" name="l00993"></a><span class="lineno"> 993</span> <span class="keywordflow">return</span> ComputeEuclideanNormLocalizedLagrangianBounds(</div>
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<div class="line"><a id="l00994" name="l00994"></a><span class="lineno"> 994</span> sharded_qp, primal_solution, dual_solution, primal_weight, radius,</div>
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<div class="line"><a id="l00995" name="l00995"></a><span class="lineno"> 995</span> *primal_product, *dual_product, use_diagonal_qp_trust_region_solver,</div>
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<div class="line"><a id="l00996" name="l00996"></a><span class="lineno"> 996</span> diagonal_qp_trust_region_solver_tolerance);</div>
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<div class="line"><a id="l00997" name="l00997"></a><span class="lineno"> 997</span> }</div>
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<div class="line"><a id="l00998" name="l00998"></a><span class="lineno"> 998</span> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#acdd38e3c9f22f127d7776920e3079eda">FATAL</a>) << <span class="stringliteral">"Unrecognized primal dual norm"</span>;</div>
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<div class="line"><a id="l00999" name="l00999"></a><span class="lineno"> 999</span> </div>
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<div class="line"><a id="l01000" name="l01000"></a><span class="lineno"> 1000</span> <span class="keywordflow">return</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html">LocalizedLagrangianBounds</a>();</div>
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<div class="line"><a id="l01001" name="l01001"></a><span class="lineno"> 1001</span>}</div>
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<div class="line"><a id="l01002" name="l01002"></a><span class="lineno"> 1002</span> </div>
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<div class="line"><a id="l01003" name="l01003"></a><span class="lineno"> 1003</span>} <span class="comment">// namespace operations_research::pdlp</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a3e1cfef60e774a81f30eaddf26a3a274"><div class="ttname"><a href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a></div><div class="ttdeci">#define CHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00495">base/logging.h:495</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a7cc25402ecd7591b4c39934dd656b1f9"><div class="ttname"><a href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a></div><div class="ttdeci">#define CHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00707">base/logging.h:707</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_accad43a85d781d53381cd53a9894b6ae"><div class="ttname"><a href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a></div><div class="ttdeci">#define LOG(severity)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00420">base/logging.h:420</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_afcaa7cadd41741bb855c2ada1d2ef927"><div class="ttname"><a href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a></div><div class="ttdeci">#define VLOG(verboselevel)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00984">base/logging.h:984</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_math_util_html_aac72849250cdf23aefdd991eb0fc0385"><div class="ttname"><a href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">operations_research::MathUtil::Square</a></div><div class="ttdeci">static T Square(const T x)</div><div class="ttdef"><b>Definition:</b> <a href="mathutil_8h_source.html#l00101">mathutil.h:101</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html">operations_research::pdlp::DiagonalTrustRegionProblemFromQp</a></div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00537">trust_region.cc:537</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp_html_a09ccf99be502491aacb4aa87583d2bdd"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a09ccf99be502491aacb4aa87583d2bdd">operations_research::pdlp::DiagonalTrustRegionProblemFromQp::Objective</a></div><div class="ttdeci">double Objective(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00584">trust_region.cc:584</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp_html_a26c142eaecb81e4a80ac5cb5d7bfc1a3"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3">operations_research::pdlp::DiagonalTrustRegionProblemFromQp::UpperBound</a></div><div class="ttdeci">double UpperBound(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00574">trust_region.cc:574</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp_html_a2e2de156de8d096f7491fb76053a2289"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a2e2de156de8d096f7491fb76053a2289">operations_research::pdlp::DiagonalTrustRegionProblemFromQp::ObjectiveMatrixDiagonalAt</a></div><div class="ttdeci">double ObjectiveMatrixDiagonalAt(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00589">trust_region.cc:589</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp_html_a3a130beba19f9a43060251fc0b031330"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a3a130beba19f9a43060251fc0b031330">operations_research::pdlp::DiagonalTrustRegionProblemFromQp::LowerBound</a></div><div class="ttdeci">double LowerBound(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00564">trust_region.cc:564</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp_html_a52ee25b9d65144642b73c47107026f37"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a52ee25b9d65144642b73c47107026f37">operations_research::pdlp::DiagonalTrustRegionProblemFromQp::DiagonalTrustRegionProblemFromQp</a></div><div class="ttdeci">DiagonalTrustRegionProblemFromQp(const QuadraticProgram *qp, const VectorXd *primal_solution, const VectorXd *dual_solution, const VectorXd *primal_gradient, const VectorXd *dual_gradient, const double primal_weight)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00541">trust_region.cc:541</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp_html_a745a6cbad664d808756705f7c7920754"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#a745a6cbad664d808756705f7c7920754">operations_research::pdlp::DiagonalTrustRegionProblemFromQp::CenterPoint</a></div><div class="ttdeci">double CenterPoint(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00555">trust_region.cc:555</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp_html_adbf3f8e0abf2f5206e3eea73a37ad6cd"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_from_qp.html#adbf3f8e0abf2f5206e3eea73a37ad6cd">operations_research::pdlp::DiagonalTrustRegionProblemFromQp::NormWeight</a></div><div class="ttdeci">double NormWeight(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00560">trust_region.cc:560</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html">operations_research::pdlp::DiagonalTrustRegionProblem</a></div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00479">trust_region.cc:479</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_html_a09ccf99be502491aacb4aa87583d2bdd"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a09ccf99be502491aacb4aa87583d2bdd">operations_research::pdlp::DiagonalTrustRegionProblem::Objective</a></div><div class="ttdeci">double Objective(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00508">trust_region.cc:508</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_html_a26c142eaecb81e4a80ac5cb5d7bfc1a3"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3">operations_research::pdlp::DiagonalTrustRegionProblem::UpperBound</a></div><div class="ttdeci">double UpperBound(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00504">trust_region.cc:504</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_html_a2e2de156de8d096f7491fb76053a2289"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a2e2de156de8d096f7491fb76053a2289">operations_research::pdlp::DiagonalTrustRegionProblem::ObjectiveMatrixDiagonalAt</a></div><div class="ttdeci">double ObjectiveMatrixDiagonalAt(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00510">trust_region.cc:510</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_html_a3a130beba19f9a43060251fc0b031330"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a3a130beba19f9a43060251fc0b031330">operations_research::pdlp::DiagonalTrustRegionProblem::LowerBound</a></div><div class="ttdeci">double LowerBound(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00500">trust_region.cc:500</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_html_a738219be743444c6ffc6fdb9802ab5a3"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a738219be743444c6ffc6fdb9802ab5a3">operations_research::pdlp::DiagonalTrustRegionProblem::DiagonalTrustRegionProblem</a></div><div class="ttdeci">DiagonalTrustRegionProblem(const VectorXd *objective_vector, const VectorXd *objective_matrix_diagonal, const VectorXd *lower_bounds, const VectorXd *upper_bounds, const VectorXd *center_point, const VectorXd *norm_weights)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00483">trust_region.cc:483</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_html_a745a6cbad664d808756705f7c7920754"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#a745a6cbad664d808756705f7c7920754">operations_research::pdlp::DiagonalTrustRegionProblem::CenterPoint</a></div><div class="ttdeci">double CenterPoint(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00496">trust_region.cc:496</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem_html_adbf3f8e0abf2f5206e3eea73a37ad6cd"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_diagonal_trust_region_problem.html#adbf3f8e0abf2f5206e3eea73a37ad6cd">operations_research::pdlp::DiagonalTrustRegionProblem::NormWeight</a></div><div class="ttdeci">double NormWeight(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00498">trust_region.cc:498</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">operations_research::pdlp::ShardedQuadraticProgram</a></div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00033">sharded_quadratic_program.h:33</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_a1e0d1154156a56084d0ba5232819b134"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a1e0d1154156a56084d0ba5232819b134">operations_research::pdlp::ShardedQuadraticProgram::TransposedConstraintMatrix</a></div><div class="ttdeci">const Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > & TransposedConstraintMatrix() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00049">sharded_quadratic_program.h:49</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_a8bf92cdb63b602aba6f4d22b975e2f30"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a8bf92cdb63b602aba6f4d22b975e2f30">operations_research::pdlp::ShardedQuadraticProgram::TransposedConstraintMatrixSharder</a></div><div class="ttdeci">const Sharder & TransposedConstraintMatrixSharder() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00058">sharded_quadratic_program.h:58</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_ab7ab55f549e3f9c1a1c8c8d2b766f75b"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">operations_research::pdlp::ShardedQuadraticProgram::PrimalSharder</a></div><div class="ttdeci">const Sharder & PrimalSharder() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00062">sharded_quadratic_program.h:62</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_ab945b88f1937277a896d4c7c7935d605"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab945b88f1937277a896d4c7c7935d605">operations_research::pdlp::ShardedQuadraticProgram::PrimalSize</a></div><div class="ttdeci">int64_t PrimalSize() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00066">sharded_quadratic_program.h:66</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_abfdc79e4b2325ff283b7d2333d40fffe"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">operations_research::pdlp::ShardedQuadraticProgram::Qp</a></div><div class="ttdeci">const QuadraticProgram & Qp() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00045">sharded_quadratic_program.h:45</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_ac9f7db642c1b4c4fc37f489f03d110a7"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ac9f7db642c1b4c4fc37f489f03d110a7">operations_research::pdlp::ShardedQuadraticProgram::ConstraintMatrixSharder</a></div><div class="ttdeci">const Sharder & ConstraintMatrixSharder() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00054">sharded_quadratic_program.h:54</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_afcafa95b1a351212291c7a030deec52a"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#afcafa95b1a351212291c7a030deec52a">operations_research::pdlp::ShardedQuadraticProgram::DualSize</a></div><div class="ttdeci">int64_t DualSize() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00067">sharded_quadratic_program.h:67</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_1_1_shard_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">operations_research::pdlp::Sharder::Shard</a></div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00055">sharder.h:55</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_1_1_shard_html_a8ef12397d1682615bc3108c397734179"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">operations_research::pdlp::Sharder::Shard::Index</a></div><div class="ttdeci">int Index() const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00127">sharder.h:127</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html">operations_research::pdlp::Sharder</a></div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00034">sharder.h:34</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html_a2e06481a59fc1f866bd6c898a696b014"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html#a2e06481a59fc1f866bd6c898a696b014">operations_research::pdlp::Sharder::ParallelSumOverShards</a></div><div class="ttdeci">double ParallelSumOverShards(const std::function< double(const Shard &)> &func) const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00131">sharder.cc:131</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html_a9761cf0a21e5b7efe9126765eec48a3a"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html#a9761cf0a21e5b7efe9126765eec48a3a">operations_research::pdlp::Sharder::ParallelTrueForAllShards</a></div><div class="ttdeci">bool ParallelTrueForAllShards(const std::function< bool(const Shard &)> &func) const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00140">sharder.cc:140</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html_a998aef9096f234a37e58caddca6db203"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html#a998aef9096f234a37e58caddca6db203">operations_research::pdlp::Sharder::ShardSize</a></div><div class="ttdeci">int64_t ShardSize(int shard) const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00186">sharder.h:186</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html_abfb02437c97584ca43c040284aecf748"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html#abfb02437c97584ca43c040284aecf748">operations_research::pdlp::Sharder::ShardStart</a></div><div class="ttdeci">int64_t ShardStart(int shard) const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00192">sharder.h:192</a></div></div>
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<div class="ttc" id="agscip__solver_8cc_html_a1ba5ca0f61f2fa13bd23bf0f89004f35"><div class="ttname"><a href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a></div><div class="ttdeci">double upper_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00137">gscip_solver.cc:137</a></div></div>
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<div class="ttc" id="agscip__solver_8cc_html_a1e2f9a2352c1d9a6cada9544898fceec"><div class="ttname"><a href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a></div><div class="ttdeci">double lower_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00136">gscip_solver.cc:136</a></div></div>
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<div class="ttc" id="alocal__search_8cc_html_a750b5d744c39a06bfb13e6eb010e35d0"><div class="ttname"><a href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a></div><div class="ttdeci">int index</div><div class="ttdef"><b>Definition:</b> <a href="local__search_8cc_source.html#l02750">local_search.cc:2750</a></div></div>
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<div class="ttc" id="alog__severity_8h_html_acdd38e3c9f22f127d7776920e3079eda"><div class="ttname"><a href="log__severity_8h.html#acdd38e3c9f22f127d7776920e3079eda">FATAL</a></div><div class="ttdeci">const int FATAL</div><div class="ttdef"><b>Definition:</b> <a href="log__severity_8h_source.html#l00032">log_severity.h:32</a></div></div>
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<div class="ttc" id="amathutil_8h_html"><div class="ttname"><a href="mathutil_8h.html">mathutil.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a1dcd08b0f6c19cd4a302bb5a3a6ea06e"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">operations_research::glop::Square</a></div><div class="ttdeci">Fractional Square(Fractional f)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00036">lp_data/lp_utils.h:36</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_1_1internal_html_a0d1a488cd88b2db320196184c8a60713"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#a0d1a488cd88b2db320196184c8a60713">operations_research::pdlp::internal::ComputeInitialUndecidedComponents</a></div><div class="ttdeci">double ComputeInitialUndecidedComponents(const TrustRegionProblem &problem, int64_t start_index, int64_t end_index, std::vector< int64_t > &undecided_components)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00246">trust_region.h:246</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_1_1internal_html_a70dfeb22c2d7bf7aac11a168f80d8bb1"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#a70dfeb22c2d7bf7aac11a168f80d8bb1">operations_research::pdlp::internal::ProjectedValue</a></div><div class="ttdeci">double ProjectedValue(const TrustRegionProblem &problem, const int64_t index, const double step_size)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00216">trust_region.h:216</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_1_1internal_html_a7d3c6d3cc8d588acbb2573e3384f3bd0"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#a7d3c6d3cc8d588acbb2573e3384f3bd0">operations_research::pdlp::internal::RemoveCriticalStepsAboveThreshold</a></div><div class="ttdeci">double RemoveCriticalStepsAboveThreshold(const TrustRegionProblem &problem, const double step_size_threshold, std::vector< int64_t > &undecided_components)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00286">trust_region.h:286</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_1_1internal_html_aa8ad95f3ab1aca8e985d46d0db21e15f"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#aa8ad95f3ab1aca8e985d46d0db21e15f">operations_research::pdlp::internal::RemoveCriticalStepsBelowThreshold</a></div><div class="ttdeci">double RemoveCriticalStepsBelowThreshold(const TrustRegionProblem &problem, const double step_size_threshold, std::vector< int64_t > &undecided_components)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00313">trust_region.h:313</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_1_1internal_html_ab8901158cf75681cf82a1d866a1118e6"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#ab8901158cf75681cf82a1d866a1118e6">operations_research::pdlp::internal::EasyMedian</a></div><div class="ttdeci">double EasyMedian(ArrayType array, ValueFunction value_function)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00230">trust_region.h:230</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_1_1internal_html_af260cca7eeddd5e8e77712bd259b3278"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#af260cca7eeddd5e8e77712bd259b3278">operations_research::pdlp::internal::RadiusSquaredOfUndecidedComponents</a></div><div class="ttdeci">double RadiusSquaredOfUndecidedComponents(const TrustRegionProblem &problem, const double step_size, const std::vector< int64_t > &undecided_components)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00267">trust_region.h:267</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html">operations_research::pdlp</a></div><div class="ttdef"><b>Definition:</b> <a href="iteration__stats_8cc_source.html#l00040">iteration_stats.cc:40</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a259d3f73717a2ababa9df2dd43914656"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a259d3f73717a2ababa9df2dd43914656">operations_research::pdlp::ComputePrimalGradient</a></div><div class="ttdeci">LagrangianPart ComputePrimalGradient(const ShardedQuadraticProgram &sharded_qp, const VectorXd &primal_solution, const VectorXd &dual_product)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00462">sharded_optimization_utils.cc:462</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a39db3ccea12adec49816af128a288223"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a39db3ccea12adec49816af128a288223">operations_research::pdlp::SolveDiagonalTrustRegionProblem</a></div><div class="ttdeci">TrustRegionResult SolveDiagonalTrustRegionProblem(const DiagonalTrustRegionProblem &problem, const Sharder &sharder, const double target_radius, const double solve_tol)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00693">trust_region.cc:693</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a39f9a12aa1bd94ddb3a56816d4d25eb0"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a39f9a12aa1bd94ddb3a56816d4d25eb0">operations_research::pdlp::PrimalDualNorm</a></div><div class="ttdeci">PrimalDualNorm</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00120">trust_region.h:120</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a3c71f00da2c898c481414c3e92f12f0d"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a3c71f00da2c898c481414c3e92f12f0d">operations_research::pdlp::NormOfDeltaProjection</a></div><div class="ttdeci">double NormOfDeltaProjection(const DiagonalTrustRegionProblem &problem, const Sharder &sharder, const double scaling_factor)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00635">trust_region.cc:635</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a463586ded0a114d3ca4b97a048d37d8a"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a463586ded0a114d3ca4b97a048d37d8a">operations_research::pdlp::TransposedMatrixVectorProduct</a></div><div class="ttdeci">VectorXd TransposedMatrixVectorProduct(const Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > &matrix, const VectorXd &vector, const Sharder &sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00151">sharder.cc:151</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a5f128477eac14f0eda4b73fdfb3e24d4"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a5f128477eac14f0eda4b73fdfb3e24d4">operations_research::pdlp::SolveDiagonalTrustRegion</a></div><div class="ttdeci">TrustRegionResult SolveDiagonalTrustRegion(const VectorXd &objective_vector, const VectorXd &objective_matrix_diagonal, const VectorXd &variable_lower_bounds, const VectorXd &variable_upper_bounds, const VectorXd &center_point, const VectorXd &norm_weights, const double target_radius, const Sharder &sharder, const double solve_tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00741">trust_region.cc:741</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a608ed26a4c7ff3bdcb22d25ff890f47d"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a608ed26a4c7ff3bdcb22d25ff890f47d">operations_research::pdlp::ComputeDualGradient</a></div><div class="ttdeci">LagrangianPart ComputeDualGradient(const ShardedQuadraticProgram &sharded_qp, const Eigen::VectorXd &dual_solution, const Eigen::VectorXd &primal_product)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00518">sharded_optimization_utils.cc:518</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a64c21ba4bf7d15e5dd1f8396074a9dfa"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a64c21ba4bf7d15e5dd1f8396074a9dfa">operations_research::pdlp::SolveDiagonalQpTrustRegion</a></div><div class="ttdeci">TrustRegionResult SolveDiagonalQpTrustRegion(const ShardedQuadraticProgram &sharded_qp, const VectorXd &primal_solution, const VectorXd &dual_solution, const VectorXd &primal_gradient, const VectorXd &dual_gradient, const double primal_weight, double target_radius, const double solve_tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00754">trust_region.cc:754</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a7bd16384c5572b001a57e9987bf5b0e9"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a7bd16384c5572b001a57e9987bf5b0e9">operations_research::pdlp::FindScalingFactor</a></div><div class="ttdeci">double FindScalingFactor(const DiagonalTrustRegionProblem &problem, const Sharder &sharder, const double target_radius, const double solve_tol)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00662">trust_region.cc:662</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a8da80544adc685ee442522ede0e095a9"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a8da80544adc685ee442522ede0e095a9">operations_research::pdlp::SolveTrustRegion</a></div><div class="ttdeci">TrustRegionResult SolveTrustRegion(const VectorXd &objective_vector, const VectorXd &variable_lower_bounds, const VectorXd &variable_upper_bounds, const VectorXd &center_point, const VectorXd &norm_weights, const double target_radius, const Sharder &sharder)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00452">trust_region.cc:452</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_accb6df46237b5d870b93c6566cadd722"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#accb6df46237b5d870b93c6566cadd722">operations_research::pdlp::ProjectedValueOfScaledDifference</a></div><div class="ttdeci">double ProjectedValueOfScaledDifference(const DiagonalTrustRegionProblem &problem, const int64_t index, const double scaling_factor)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00615">trust_region.cc:615</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_adb77e7cede2fecf6bccfa93226b49c0b"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#adb77e7cede2fecf6bccfa93226b49c0b">operations_research::pdlp::ComputeLocalizedLagrangianBounds</a></div><div class="ttdeci">LocalizedLagrangianBounds ComputeLocalizedLagrangianBounds(const ShardedQuadraticProgram &sharded_qp, const VectorXd &primal_solution, const VectorXd &dual_solution, const PrimalDualNorm primal_dual_norm, const double primal_weight, const double radius, const VectorXd *primal_product, const VectorXd *dual_product, const bool use_diagonal_qp_trust_region_solver, const double diagonal_qp_trust_region_solver_tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00963">trust_region.cc:963</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a3ad49ae9019c528851f6fd084479a567"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a3ad49ae9019c528851f6fd084479a567">operations_research::sat::LowerBound</a></div><div class="ttdeci">std::function< int64_t(const Model &)> LowerBound(IntegerVariable v)</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l01663">integer.h:1663</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a9e815eb2193f1bb6903274c7f0859cd7"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a9e815eb2193f1bb6903274c7f0859cd7">operations_research::sat::UpperBound</a></div><div class="ttdeci">std::function< int64_t(const Model &)> UpperBound(IntegerVariable v)</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l01669">integer.h:1669</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_abb66766a5d79e878ff67851bc55ca24f"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#abb66766a5d79e878ff67851bc55ca24f">operations_research::sat::ComputeObjectiveValue</a></div><div class="ttdeci">Coefficient ComputeObjectiveValue(const LinearBooleanProblem &problem, const std::vector< bool > &assignment)</div><div class="ttdef"><b>Definition:</b> <a href="boolean__problem_8cc_source.html#l00359">boolean_problem.cc:359</a></div></div>
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<div class="ttc" id="apack_8cc_html_a4255f714cea26cdd64f6a0ee72d34a8c"><div class="ttname"><a href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a></div><div class="ttdeci">int64_t weight</div><div class="ttdef"><b>Definition:</b> <a href="pack_8cc_source.html#l00510">pack.cc:510</a></div></div>
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<div class="ttc" id="aquadratic__program_8h_html"><div class="ttname"><a href="quadratic__program_8h.html">quadratic_program.h</a></div></div>
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<div class="ttc" id="asat_2lp__utils_8cc_html_a561d7bf12fc7674b3fe0ad2ba2e175a0"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a></div><div class="ttdeci">std::vector< double > lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00606">sat/lp_utils.cc:606</a></div></div>
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<div class="ttc" id="asat_2lp__utils_8cc_html_a88215c8581662c40eec0fb8621c44af3"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a></div><div class="ttdeci">std::vector< double > upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00607">sat/lp_utils.cc:607</a></div></div>
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<div class="ttc" id="asearch_8cc_html_a9c6d2505b571d11bc113813060f465a3"><div class="ttname"><a href="search_8cc.html#a9c6d2505b571d11bc113813060f465a3">objective_</a></div><div class="ttdeci">IntVar *const objective_</div><div class="ttdef"><b>Definition:</b> <a href="search_8cc_source.html#l03017">search.cc:3017</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8h_html"><div class="ttname"><a href="sharded__optimization__utils_8h.html">sharded_optimization_utils.h</a></div></div>
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<div class="ttc" id="asharded__quadratic__program_8h_html"><div class="ttname"><a href="sharded__quadratic__program_8h.html">sharded_quadratic_program.h</a></div></div>
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<div class="ttc" id="asharder_8h_html"><div class="ttname"><a href="sharder_8h.html">sharder.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html">operations_research::pdlp::LocalizedLagrangianBounds</a></div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00102">trust_region.h:102</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">operations_research::pdlp::QuadraticProgram</a></div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00054">quadratic_program.h:54</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_ae7a462ef3035095eff6c883ae0078d02"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae7a462ef3035095eff6c883ae0078d02">operations_research::pdlp::QuadraticProgram::constraint_matrix</a></div><div class="ttdeci">Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > constraint_matrix</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00131">quadratic_program.h:131</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_trust_region_result_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_trust_region_result.html">operations_research::pdlp::TrustRegionResult</a></div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00032">trust_region.h:32</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_trust_region_result_html_a879215ecd0117ade78436fc4590747e0"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a879215ecd0117ade78436fc4590747e0">operations_research::pdlp::TrustRegionResult::solution_step_size</a></div><div class="ttdeci">double solution_step_size</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00034">trust_region.h:34</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_trust_region_result_html_a92098f9990f978c61c5dcb88815f008e"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a92098f9990f978c61c5dcb88815f008e">operations_research::pdlp::TrustRegionResult::solution</a></div><div class="ttdeci">Eigen::VectorXd solution</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00045">trust_region.h:45</a></div></div>
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<div class="ttc" id="atrust__region_8cc_html_a35a93e273ed07f347699c3f4b4b5f581"><div class="ttname"><a href="trust__region_8cc.html#a35a93e273ed07f347699c3f4b4b5f581">trust_region_objective_delta</a></div><div class="ttdeci">double trust_region_objective_delta</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00795">trust_region.cc:795</a></div></div>
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<div class="ttc" id="atrust__region_8cc_html_a59572487cff4d7cb15cdabbffd9685b2"><div class="ttname"><a href="trust__region_8cc.html#a59572487cff4d7cb15cdabbffd9685b2">part_of_lagrangian_value</a></div><div class="ttdeci">double part_of_lagrangian_value</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00786">trust_region.cc:786</a></div></div>
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<div class="ttc" id="atrust__region_8cc_html_a69703b8569462134ad4e22ab0133e418"><div class="ttname"><a href="trust__region_8cc.html#a69703b8569462134ad4e22ab0133e418">objective_value</a></div><div class="ttdeci">double objective_value</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00167">trust_region.cc:167</a></div></div>
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<div class="ttc" id="atrust__region_8cc_html_a8537e4c5ab72a497c1f81fad8c3b1db6"><div class="ttname"><a href="trust__region_8cc.html#a8537e4c5ab72a497c1f81fad8c3b1db6">undecided_components_by_shard</a></div><div class="ttdeci">std::vector< std::vector< int64_t > > undecided_components_by_shard</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00205">trust_region.cc:205</a></div></div>
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<div class="ttc" id="atrust__region_8cc_html_a879215ecd0117ade78436fc4590747e0"><div class="ttname"><a href="trust__region_8cc.html#a879215ecd0117ade78436fc4590747e0">solution_step_size</a></div><div class="ttdeci">double solution_step_size</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00165">trust_region.cc:165</a></div></div>
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<div class="ttc" id="atrust__region_8cc_html_a9f97b60109cf3b1650acf7fa8b5dd307"><div class="ttname"><a href="trust__region_8cc.html#a9f97b60109cf3b1650acf7fa8b5dd307">radius_coefficient_of_decided_components</a></div><div class="ttdeci">double radius_coefficient_of_decided_components</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8cc_source.html#l00206">trust_region.cc:206</a></div></div>
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<div class="ttc" id="atrust__region_8h_html"><div class="ttname"><a href="trust__region_8h.html">trust_region.h</a></div></div>
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<div class="ttc" id="atrust__region__test_8cc_html_a16346c4c462dec8f0cf38493c5e0358c"><div class="ttname"><a href="trust__region__test_8cc.html#a16346c4c462dec8f0cf38493c5e0358c">variable_lower_bounds</a></div><div class="ttdeci">VectorXd variable_lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="trust__region__test_8cc_source.html#l00863">trust_region_test.cc:863</a></div></div>
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<div class="ttc" id="atrust__region__test_8cc_html_a2cc94fcc3b7abf4cdc59197b0c10cefe"><div class="ttname"><a href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a></div><div class="ttdeci">VectorXd center_point</div><div class="ttdef"><b>Definition:</b> <a href="trust__region__test_8cc_source.html#l00862">trust_region_test.cc:862</a></div></div>
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<div class="ttc" id="atrust__region__test_8cc_html_a868af74445e29f368ccf4a9e053f9267"><div class="ttname"><a href="trust__region__test_8cc.html#a868af74445e29f368ccf4a9e053f9267">variable_upper_bounds</a></div><div class="ttdeci">VectorXd variable_upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="trust__region__test_8cc_source.html#l00864">trust_region_test.cc:864</a></div></div>
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<div class="ttc" id="atrust__region__test_8cc_html_ac824522e23b1d307c272d07493af3a65"><div class="ttname"><a href="trust__region__test_8cc.html#ac824522e23b1d307c272d07493af3a65">objective_vector</a></div><div class="ttdeci">VectorXd objective_vector</div><div class="ttdef"><b>Definition:</b> <a href="trust__region__test_8cc_source.html#l00860">trust_region_test.cc:860</a></div></div>
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<div class="ttc" id="atrust__region__test_8cc_html_ad31783425c63eac33cc6aade41a6537d"><div class="ttname"><a href="trust__region__test_8cc.html#ad31783425c63eac33cc6aade41a6537d">norm_weights</a></div><div class="ttdeci">VectorXd norm_weights</div><div class="ttdef"><b>Definition:</b> <a href="trust__region__test_8cc_source.html#l00865">trust_region_test.cc:865</a></div></div>
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<div class="ttc" id="atrust__region__test_8cc_html_ad8dc72e7835d167fffffac5769c55076"><div class="ttname"><a href="trust__region__test_8cc.html#ad8dc72e7835d167fffffac5769c55076">objective_matrix_diagonal</a></div><div class="ttdeci">VectorXd objective_matrix_diagonal</div><div class="ttdef"><b>Definition:</b> <a href="trust__region__test_8cc_source.html#l00861">trust_region_test.cc:861</a></div></div>
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