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<div class="headertitle"><div class="title">trust_region.h</div></div>
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<a href="trust__region_8h.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">#ifndef PDLP_TRUST_REGION_H_</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define PDLP_TRUST_REGION_H_</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <cmath></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <limits></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/algorithm/container.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="sharded__quadratic__program_8h.html">ortools/pdlp/sharded_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="sharder_8h.html">ortools/pdlp/sharder.h</a>"</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</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="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"><a class="line" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html"> 32</a></span><span class="keyword">struct </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="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// The step_size of the solution.</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a879215ecd0117ade78436fc4590747e0"> 34</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a879215ecd0117ade78436fc4590747e0">solution_step_size</a>;</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// The value objective_vector' * (solution - center_point)</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// when using the linear-time solver for LPs and QPs with objective matrix not</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// treated in the prox term. When using the approximate solver for QPs, this</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// field contains the value</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// 0.5 * (solution - center_point)' * objective_matrix * (</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// solution - center_point)</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// + objective_vector' * (solution - center_point)</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// instead.</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a69703b8569462134ad4e22ab0133e418"> 43</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a69703b8569462134ad4e22ab0133e418">objective_value</a>;</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// The solution.</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a92098f9990f978c61c5dcb88815f008e"> 45</a></span> Eigen::VectorXd <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a92098f9990f978c61c5dcb88815f008e">solution</a>;</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span>};</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> </div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// Solves the following trust-region problem with bound constraints:</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// min_x objective_vector' * (x - center_point)</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// s.t. variable_lower_bounds <= x <= variable_upper_bounds</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// || x - center_point ||_W <= target_radius</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// where ||y||_W = sqrt(sum_i norm_weights[i] * y[i]^2)</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// using an exact linear-time method.</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// The sharder should have the same size as the number of variables in the</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">// problem.</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// Assumes that there is always a feasible solution, that is, that</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment">// variable_lower_bounds <= center_point <= variable_upper_bounds, and that</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// norm_weights > 0, for 0 <= i < sharder.NumElements().</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a90dd3b503fb3d2bb8bd51729584d6bad"> 59</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> Eigen::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="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">const</span> Eigen::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="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">const</span> Eigen::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="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">const</span> Eigen::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="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">const</span> Eigen::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="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordtype">double</span> target_radius,</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</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="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">// Solves the following trust-region problem with bound constraints:</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</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="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment">// + objective_vector' * (x - center_point)</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment">// s.t. variable_lower_bounds <= x <= variable_upper_bounds</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="comment">// || x - center_point ||_W <= target_radius</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="comment">// where ||y||_W = sqrt(sum_i norm_weights[i] * y[i]^2).</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment">// It replaces the ball constraint || x - center_point ||_W <= target_radius</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment">// with the equivalent constraint 0.5 * || x - center_point ||_W^2 <= 0.5 *</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment">// target_radius^2 and does a binary search for a Lagrange multiplier for the</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">// latter constraint that is at most `solve_tolerance * max(1, lambda*)` away</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">// from the optimum Lagrange multiplier lambda*.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment">// The sharder should have the same size as the number of variables in the</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment">// problem.</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment">// Assumes that there is always a feasible solution, that is, that</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="comment">// variable_lower_bounds <= center_point <= variable_upper_bounds, and that</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment">// norm_weights > 0, for 0 <= i < sharder.NumElements().</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#ad87e72f6888d8bd27a4d74f35c3a118d"> 83</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="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keyword">const</span> Eigen::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="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">const</span> Eigen::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="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">const</span> Eigen::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="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keyword">const</span> Eigen::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="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keyword">const</span> Eigen::VectorXd& <a class="code hl_variable" href="trust__region__test_8cc.html#a2cc94fcc3b7abf4cdc59197b0c10cefe">center_point</a>, <span class="keyword">const</span> Eigen::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="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordtype">double</span> target_radius, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a>& sharder, <span class="keywordtype">double</span> solve_tolerance);</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="comment">// Like SolveDiagonalTrustRegion, but extracts the problem data from a</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">// ShardedQuadraticProgram and implicitly concatenates the primal and dual parts</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="comment">// before solving the trust-region subproblem.</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a2f4054cb0abdfaacfebe5bf1b67eb9c9"> 94</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="l00095" name="l00095"></a><span class="lineno"> 95</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,</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keyword">const</span> Eigen::VectorXd& primal_solution,</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">const</span> Eigen::VectorXd& dual_solution,</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">const</span> Eigen::VectorXd& primal_gradient,</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">const</span> Eigen::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="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordtype">double</span> target_radius, <span class="keywordtype">double</span> solve_tolerance);</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html"> 102</a></span><span class="keyword">struct </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="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// The value of the Lagrangian function L(x, y) at the given solution.</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#ad16c3e3b8e83fc9a72f8309bc63534b2"> 104</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#ad16c3e3b8e83fc9a72f8309bc63534b2">lagrangian_value</a>;</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// A lower bound on the Lagrangian value, valid for the given radius.</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a1e2f9a2352c1d9a6cada9544898fceec"> 106</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>;</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// An upper bound on the Lagrangian value, valid for the given radius.</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a1ba5ca0f61f2fa13bd23bf0f89004f35"> 108</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>;</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// The radius used when computing the bounds.</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a3f67c53b80389c5f53961936edba04c9"> 110</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a3f67c53b80389c5f53961936edba04c9">radius</a>;</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span>};</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#afdd1506c32f697aeb13c4b9a9f05ba03"> 113</a></span><span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#afdd1506c32f697aeb13c4b9a9f05ba03">BoundGap</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html">LocalizedLagrangianBounds</a>& <a class="code hl_variable" href="cp__model__solver_8cc.html#a06dad0852d85b0686e01c084207c03a7">bounds</a>) {</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="cp__model__solver_8cc.html#a06dad0852d85b0686e01c084207c03a7">bounds</a>.upper_bound - <a class="code hl_variable" href="cp__model__solver_8cc.html#a06dad0852d85b0686e01c084207c03a7">bounds</a>.lower_bound;</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span>}</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">// Defines a norm on a vector partitioned as (x, y) where x is the primal and y</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment">// is the dual. The enum values define a joint norm as a function of ||x||_P and</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment">// ||y||_D, whose definition depends on the context.</span></div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a39f9a12aa1bd94ddb3a56816d4d25eb0"> 120</a></span><span class="keyword">enum class</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1pdlp.html#a39f9a12aa1bd94ddb3a56816d4d25eb0">PrimalDualNorm</a> {</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// The joint norm ||(x,y)||_PD = max{||x||_P, ||y||_D}.</span></div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1pdlp.html#a39f9a12aa1bd94ddb3a56816d4d25eb0a974f1270f89b99d15b58a4d35c26aedc">kMaxNorm</a>,</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="comment">// The joint norm (||(x,y)||_PD)^2 = (||x||_P)^2 + (||y||_D)^2.</span></div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1pdlp.html#a39f9a12aa1bd94ddb3a56816d4d25eb0aaafbdb17e2f1da89be62331fa0cf5503">kEuclideanNorm</a></div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span>};</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="comment">// Recall the saddle-point formulation OPT = min_x max_y L(x, y) defined at</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><span class="comment">// https://developers.google.com/optimization/lp/pdlp_math#saddle-point_formulation.</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="comment">// This function computes lower and upper bounds on OPT with an additional ball</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="comment">// or "trust- region" constraint on the domains of x and y.</span></div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="comment">//</span></div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span><span class="comment">// The bounds are derived from the solution of the following problem:</span></div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><span class="comment">// min_{x,y} ∇_x L(primal_solution, dual_solution)^T (x - primal_solution) -</span></div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</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="l00135" name="l00135"></a><span class="lineno"> 135</span><span class="comment">// subject to ||(x - primal_solution, y - dual_solution)||_PD <= radius,</span></div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="comment">// where x and y are constrained to their respective bounds and ||(x,y)||_PD is</span></div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="comment">// defined by primal_dual_norm.</span></div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="comment">// When use_diagonal_qp_trust_region_solver is true, the solver instead solves</span></div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span><span class="comment">// the following problem:</span></div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="comment">// min_{x,y} ∇_x L(primal_solution, dual_solution)^T (x - primal_solution) -</span></div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</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="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment">// (1 / 2) * (x - primal_solution)^T * objective_matrix * (x - primal_solution),</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment">// subject to ||(x - primal_solution, y - dual_solution)||_PD <= radius.</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="comment">// use_diagonal_qp_trust_region_solver == true assumes that primal_dual_norm</span></div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="comment">// is the Euclidean norm and the objective matrix is diagonal.</span></div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span><span class="comment">// See SolveDiagonalTrustRegion() above for the meaning of</span></div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="comment">// diagonal_qp_trust_region_solver_tolerance.</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="comment">//</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="comment">// In the context of primal_dual_norm, the primal norm ||.||_P is defined as</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="comment">// (||x||_P)^2 = (1 / 2) * primal_weight * ||x||_2^2, and the dual norm ||.||_D</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="comment">// is defined as</span></div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="comment">// (||y||_D)^2 = (1 / 2) * (1 / primal_weight) * ||y||_2^2.</span></div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span><span class="comment">//</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="comment">// Given an optimal solution (x, y) to the above problem, the lower bound is</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="comment">// computed as L(primal_solution, dual_solution) +</span></div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="comment">// ∇_x L(primal_solution, dual_solution)^T (x - primal_solution)</span></div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="comment">// and the upper bound is computed as L(primal_solution, dual_solution) +</span></div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</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="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="comment">//</span></div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="comment">// The bounds are "localized" because they are guaranteed to bound OPT only if</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="comment">// the ||.||_PD ball contains an optimal solution.</span></div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span><span class="comment">// The primal_product and dual_product arguments optionally specify the values</span></div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="comment">// of constraint_matrix * primal_solution and constraint_matrix.transpose() *</span></div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="comment">// dual_solution, respectively. If set to nullptr, they will be computed.</span></div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#aca670cd122efdc372993d4b49568ec4f"> 165</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="l00166" name="l00166"></a><span class="lineno"> 166</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,</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keyword">const</span> Eigen::VectorXd& primal_solution,</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keyword">const</span> Eigen::VectorXd& dual_solution, <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="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordtype">double</span> primal_weight, <span class="keywordtype">double</span> radius, <span class="keyword">const</span> Eigen::VectorXd* primal_product,</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="keyword">const</span> Eigen::VectorXd* dual_product,</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="keywordtype">bool</span> use_diagonal_qp_trust_region_solver,</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordtype">double</span> diagonal_qp_trust_region_solver_tolerance);</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> </div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceinternal.html">internal</a> {</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span><span class="comment">// These functions templated on TrustRegionProblem compute values useful to the</span></div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="comment">// trust region solve. The templated TrustRegionProblem type should provide</span></div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span><span class="comment">// methods:</span></div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span><span class="comment">// double Objective(int64_t index) const;</span></div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span><span class="comment">// double LowerBound(int64_t index) const;</span></div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span><span class="comment">// double UpperBound(int64_t index) const;</span></div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span><span class="comment">// double CenterPoint(int64_t index) const;</span></div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span><span class="comment">// double NormWeight(int64_t index) const;</span></div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span><span class="comment">// See trust_region.cc for more details and several implementations.</span></div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> </div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span><span class="comment">// The distance (in the indexed element) from the center point to the bound, in</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span><span class="comment">// the direction that reduces the objective.</span></div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a89e736fe381fad1600024fa36345650b"> 189</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a89e736fe381fad1600024fa36345650b">DistanceAtCriticalStepSize</a>(<span class="keyword">const</span> TrustRegionProblem& problem,</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <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="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="keywordflow">if</span> (problem.Objective(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) == 0.0) {</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keywordflow">return</span> 0.0;</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> }</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">if</span> (problem.Objective(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) > 0.0) {</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keywordflow">return</span> problem.LowerBound(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) - 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="l00196" name="l00196"></a><span class="lineno"> 196</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="keywordflow">return</span> problem.UpperBound(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) - 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="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>}</div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span><span class="comment">// The critical step size is the step size at which the indexed element hits its</span></div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span><span class="comment">// bound (or infinity if that doesn't happen).</span></div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a8cbe1743f36aed0a68c446f0392ec93c"> 204</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a8cbe1743f36aed0a68c446f0392ec93c">CriticalStepSize</a>(<span class="keyword">const</span> TrustRegionProblem& problem,</div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <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="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="keywordflow">if</span> (problem.Objective(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) == 0.0) {</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keywordflow">return</span> std::numeric_limits<double>::infinity();</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="keywordflow">return</span> -problem.NormWeight(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) *</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a89e736fe381fad1600024fa36345650b">DistanceAtCriticalStepSize</a>(problem, <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) / 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="l00211" name="l00211"></a><span class="lineno"> 211</span>}</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span><span class="comment">// The value of the indexed element at the given step_size, projected onto the</span></div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span><span class="comment">// bounds.</span></div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a70dfeb22c2d7bf7aac11a168f80d8bb1"> 216</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a70dfeb22c2d7bf7aac11a168f80d8bb1">ProjectedValue</a>(<span class="keyword">const</span> TrustRegionProblem& 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="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">const</span> <span class="keywordtype">double</span> step_size) {</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">const</span> <span class="keywordtype">double</span> full_step =</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</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="l00220" name="l00220"></a><span class="lineno"> 220</span> step_size * problem.Objective(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) / problem.NormWeight(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(<a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(full_step, problem.LowerBound(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)),</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> problem.UpperBound(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>));</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="comment">// An easy way of computing medians that's slightly off when the length of the</span></div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span><span class="comment">// array is even. "array" is intentionally passed by copy.</span></div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span><span class="comment">// "value_function" maps an element of "array" to its (double) value. Returns</span></div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span><span class="comment">// the value of the median element.</span></div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span><span class="keyword">template</span> <<span class="keyword">typename</span> ArrayType, <span class="keyword">typename</span> ValueFunction></div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp_1_1internal.html#ab8901158cf75681cf82a1d866a1118e6"> 230</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#ab8901158cf75681cf82a1d866a1118e6">EasyMedian</a>(ArrayType array, ValueFunction value_function) {</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <a class="code hl_define" href="base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6">CHECK_GT</a>(array.size(), 0);</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keyword">auto</span> middle = array.begin() + (array.size() / 2);</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> absl::c_nth_element(array, middle,</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> [&](<span class="keyword">typename</span> ArrayType::value_type lhs,</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="keyword">typename</span> ArrayType::value_type rhs) {</div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="keywordflow">return</span> value_function(lhs) < value_function(rhs);</div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> });</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keywordflow">return</span> value_function(*middle);</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span>}</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> </div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span><span class="comment">// Lists the undecided components (from [start_index, end_index) as those with</span></div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span><span class="comment">// finite critical step sizes. The components with infinite critical step sizes</span></div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span><span class="comment">// will never hit their bounds, so returns their contribution to square of the</span></div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span><span class="comment">// radius.</span></div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a0d1a488cd88b2db320196184c8a60713"> 246</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a0d1a488cd88b2db320196184c8a60713">ComputeInitialUndecidedComponents</a>(</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keyword">const</span> TrustRegionProblem& problem, int64_t start_index, int64_t end_index,</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> std::vector<int64_t>& undecided_components) {</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="comment">// TODO(user): Evaluate dropping this reserve(), since it wastes space</span></div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// if many components are decided.</span></div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> undecided_components.clear();</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> undecided_components.reserve(end_index - start_index);</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keywordtype">double</span> radius_coefficient = 0.0;</div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keywordflow">for</span> (int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> = start_index; <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < end_index; ++<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) {</div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keywordflow">if</span> (std::isfinite(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a8cbe1743f36aed0a68c446f0392ec93c">internal::CriticalStepSize</a>(problem, <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>))) {</div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> undecided_components.push_back(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="comment">// Simplified from norm_weight * (objective / norm_weight)^2.</span></div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> radius_coefficient += <a class="code hl_function" href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">MathUtil::Square</a>(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="l00260" name="l00260"></a><span class="lineno"> 260</span> problem.NormWeight(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> }</div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> }</div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="keywordflow">return</span> radius_coefficient;</div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span>}</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="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp_1_1internal.html#af260cca7eeddd5e8e77712bd259b3278"> 267</a></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="l00268" name="l00268"></a><span class="lineno"> 268</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="l00269" name="l00269"></a><span class="lineno"> 269</span> <span class="keyword">const</span> std::vector<int64_t>& undecided_components) {</div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="keywordflow">return</span> absl::c_accumulate(</div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> undecided_components, 0.0, [&](<span class="keywordtype">double</span> sum, 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="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keyword">const</span> <span class="keywordtype">double</span> distance_at_projected_value =</div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</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="l00274" name="l00274"></a><span class="lineno"> 274</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="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keywordflow">return</span> sum + problem.NormWeight(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) *</div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <a class="code hl_function" href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">MathUtil::Square</a>(distance_at_projected_value);</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>}</div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> </div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span><span class="comment">// Points whose critical step-sizes are greater than or equal to</span></div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span><span class="comment">// step_size_threshold are eliminated from the undecided components (we know</span></div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span><span class="comment">// they'll be determined by center_point - step_size * objective /</span></div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span><span class="comment">// norm_weights). Returns the coefficient of step_size^2 that accounts of the</span></div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span><span class="comment">// contribution of the removed variables to the radius squared.</span></div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a7d3c6d3cc8d588acbb2573e3384f3bd0"> 286</a></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="l00287" name="l00287"></a><span class="lineno"> 287</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="l00288" name="l00288"></a><span class="lineno"> 288</span> std::vector<int64_t>& undecided_components) {</div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="keywordtype">double</span> variable_radius_coefficient = 0.0;</div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> : undecided_components) {</div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a8cbe1743f36aed0a68c446f0392ec93c">internal::CriticalStepSize</a>(problem, <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) >= step_size_threshold) {</div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="comment">// Simplified from norm_weight * (objective / norm_weight)^2.</span></div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> variable_radius_coefficient +=</div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <a class="code hl_function" href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">MathUtil::Square</a>(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="l00295" name="l00295"></a><span class="lineno"> 295</span> problem.NormWeight(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> }</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> }</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <span class="keyword">auto</span> result =</div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> std::remove_if(undecided_components.begin(), undecided_components.end(),</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> [&](<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="l00301" name="l00301"></a><span class="lineno"> 301</span> return internal::CriticalStepSize(problem, index) >=</div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> step_size_threshold;</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> });</div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> undecided_components.erase(result, undecided_components.end());</div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="keywordflow">return</span> variable_radius_coefficient;</div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span>}</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><span class="comment">// Points whose critical step-sizes are smaller than or equal to</span></div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span><span class="comment">// step_size_threshold are eliminated from the undecided components (we know</span></div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span><span class="comment">// they'll always be at their bounds). Returns the weighted distance squared</span></div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span><span class="comment">// from the center point for the removed components.</span></div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span><span class="keyword">template</span> <<span class="keyword">typename</span> TrustRegionProblem></div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp_1_1internal.html#aa8ad95f3ab1aca8e985d46d0db21e15f"> 313</a></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="l00314" name="l00314"></a><span class="lineno"> 314</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="l00315" name="l00315"></a><span class="lineno"> 315</span> std::vector<int64_t>& undecided_components) {</div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> <span class="keywordtype">double</span> radius_sq = 0.0;</div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> : undecided_components) {</div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a8cbe1743f36aed0a68c446f0392ec93c">internal::CriticalStepSize</a>(problem, <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) <= step_size_threshold) {</div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> radius_sq += problem.NormWeight(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) *</div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <a class="code hl_function" href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">MathUtil::Square</a>(</div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a89e736fe381fad1600024fa36345650b">internal::DistanceAtCriticalStepSize</a>(problem, <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>));</div>
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> }</div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> }</div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> <span class="keyword">auto</span> result =</div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> std::remove_if(undecided_components.begin(), undecided_components.end(),</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> [&](<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="l00327" name="l00327"></a><span class="lineno"> 327</span> return internal::CriticalStepSize(problem, index) <=</div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> step_size_threshold;</div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> });</div>
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> undecided_components.erase(result, undecided_components.end());</div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> <span class="keywordflow">return</span> radius_sq;</div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span>}</div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> </div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span><span class="comment">// PrimalTrustRegionProblem defines the primal trust region problem given a</span></div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span><span class="comment">// QuadraticProgram, primal solution, and primal gradient. It captures const</span></div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span><span class="comment">// references to the constructor arguments, which should outlive the class</span></div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span><span class="comment">// instance.</span></div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span><span class="comment">// The corresponding trust region problem is</span></div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span><span class="comment">// min_x primal_gradient' * (x - primal_solution)</span></div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</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="l00341" name="l00341"></a><span class="lineno"> 341</span><span class="comment">// || x - primal_solution ||_2 <= target_radius</span></div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html"> 342</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html">PrimalTrustRegionProblem</a> {</div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a3cd894d3cf53f1e2e43070f945d08ef4"> 344</a></span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a3cd894d3cf53f1e2e43070f945d08ef4">PrimalTrustRegionProblem</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="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="keyword">const</span> Eigen::VectorXd* primal_solution,</div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> <span class="keyword">const</span> Eigen::VectorXd* primal_gradient,</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> <span class="keyword">const</span> <span class="keywordtype">double</span> norm_weight = 1.0)</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> : qp_(*qp),</div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> primal_solution_(*primal_solution),</div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> primal_gradient_(*primal_gradient),</div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> norm_weight_(norm_weight) {}</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a09ccf99be502491aacb4aa87583d2bdd"> 352</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_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> 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="l00353" name="l00353"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a3a130beba19f9a43060251fc0b031330"> 353</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_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="l00354" name="l00354"></a><span class="lineno"> 354</span> <span class="keywordflow">return</span> qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">variable_lower_bounds</a>[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>];</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> }</div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3"> 356</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_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="l00357" name="l00357"></a><span class="lineno"> 357</span> <span class="keywordflow">return</span> qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a097d329b7af662bea9b5a8e310a22726">variable_upper_bounds</a>[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>];</div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> }</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a745a6cbad664d808756705f7c7920754"> 359</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_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> 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="l00360" name="l00360"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#adbf3f8e0abf2f5206e3eea73a37ad6cd"> 360</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_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_; }</div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> </div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</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="l00364" name="l00364"></a><span class="lineno"> 364</span> <span class="keyword">const</span> Eigen::VectorXd& primal_solution_;</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> <span class="keyword">const</span> Eigen::VectorXd& primal_gradient_;</div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="keyword">const</span> <span class="keywordtype">double</span> norm_weight_;</div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span>};</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">// DualTrustRegionProblem defines the dual trust region problem given a</span></div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span><span class="comment">// QuadraticProgram, dual solution, and dual gradient. It captures const</span></div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span><span class="comment">// references to the constructor arguments, which should outlive the class</span></div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span><span class="comment">// instance.</span></div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span><span class="comment">// The corresponding trust region problem is</span></div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span><span class="comment">// max_y dual_gradient' * (y - dual_solution)</span></div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span><span class="comment">// s.t. qp.implicit_dual_lower_bounds <= y <= qp.implicit_dual_upper_bounds</span></div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span><span class="comment">// || y - dual_solution ||_2 <= target_radius</span></div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span><span class="comment">// where the implicit dual bounds are those given in</span></div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</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="l00379" name="l00379"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html"> 379</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html">DualTrustRegionProblem</a> {</div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a92ef4bbdc88ed545a37796c2cf0de8c4"> 381</a></span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a92ef4bbdc88ed545a37796c2cf0de8c4">DualTrustRegionProblem</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="l00382" name="l00382"></a><span class="lineno"> 382</span> <span class="keyword">const</span> Eigen::VectorXd* dual_solution,</div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> <span class="keyword">const</span> Eigen::VectorXd* dual_gradient,</div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> <span class="keyword">const</span> <span class="keywordtype">double</span> norm_weight = 1.0)</div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> : qp_(*qp),</div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> dual_solution_(*dual_solution),</div>
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<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> dual_gradient_(*dual_gradient),</div>
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<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> norm_weight_(norm_weight) {}</div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a09ccf99be502491aacb4aa87583d2bdd"> 389</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_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>{</div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <span class="comment">// The objective is negated because the trust region problem objective is</span></div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="comment">// minimize, but for the dual problem we want to maximize the gradient.</span></div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> <span class="keywordflow">return</span> -dual_gradient_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>];</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"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a3a130beba19f9a43060251fc0b031330"> 394</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_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="l00395" name="l00395"></a><span class="lineno"> 395</span> <span class="keywordflow">return</span> std::isfinite(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">constraint_upper_bounds</a>[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>])</div>
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<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> ? -std::numeric_limits<double>::infinity()</div>
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<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> : 0.0;</div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> }</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3"> 399</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_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="l00400" name="l00400"></a><span class="lineno"> 400</span> <span class="keywordflow">return</span> std::isfinite(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">constraint_lower_bounds</a>[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>])</div>
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<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> ? std::numeric_limits<double>::infinity()</div>
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<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> : 0.0;</div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> }</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a745a6cbad664d808756705f7c7920754"> 404</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_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> dual_solution_[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]; }</div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#adbf3f8e0abf2f5206e3eea73a37ad6cd"> 405</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_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_; }</div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> </div>
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<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> <span class="keyword">private</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> <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="l00409" name="l00409"></a><span class="lineno"> 409</span> <span class="keyword">const</span> Eigen::VectorXd& dual_solution_;</div>
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<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <span class="keyword">const</span> Eigen::VectorXd& dual_gradient_;</div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <span class="keyword">const</span> <span class="keywordtype">double</span> norm_weight_;</div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span>};</div>
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<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> </div>
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<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span>} <span class="comment">// namespace internal</span></div>
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<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> </div>
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<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span>} <span class="comment">// namespace operations_research::pdlp</span></div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> </div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span><span class="preprocessor">#endif </span><span class="comment">// PDLP_TRUST_REGION_H_</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_a7e03ec13560fa94a8fea569960d7efc6"><div class="ttname"><a href="base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6">CHECK_GT</a></div><div class="ttdeci">#define CHECK_GT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00708">base/logging.h:708</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_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_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_1internal_1_1_dual_trust_region_problem_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html">operations_research::pdlp::internal::DualTrustRegionProblem</a></div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00379">trust_region.h:379</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem_html_a09ccf99be502491aacb4aa87583d2bdd"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a09ccf99be502491aacb4aa87583d2bdd">operations_research::pdlp::internal::DualTrustRegionProblem::Objective</a></div><div class="ttdeci">double Objective(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00389">trust_region.h:389</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem_html_a26c142eaecb81e4a80ac5cb5d7bfc1a3"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3">operations_research::pdlp::internal::DualTrustRegionProblem::UpperBound</a></div><div class="ttdeci">double UpperBound(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00399">trust_region.h:399</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem_html_a3a130beba19f9a43060251fc0b031330"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a3a130beba19f9a43060251fc0b031330">operations_research::pdlp::internal::DualTrustRegionProblem::LowerBound</a></div><div class="ttdeci">double LowerBound(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00394">trust_region.h:394</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem_html_a745a6cbad664d808756705f7c7920754"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a745a6cbad664d808756705f7c7920754">operations_research::pdlp::internal::DualTrustRegionProblem::CenterPoint</a></div><div class="ttdeci">double CenterPoint(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00404">trust_region.h:404</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem_html_a92ef4bbdc88ed545a37796c2cf0de8c4"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#a92ef4bbdc88ed545a37796c2cf0de8c4">operations_research::pdlp::internal::DualTrustRegionProblem::DualTrustRegionProblem</a></div><div class="ttdeci">DualTrustRegionProblem(const QuadraticProgram *qp, const Eigen::VectorXd *dual_solution, const Eigen::VectorXd *dual_gradient, const double norm_weight=1.0)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00381">trust_region.h:381</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem_html_adbf3f8e0abf2f5206e3eea73a37ad6cd"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_dual_trust_region_problem.html#adbf3f8e0abf2f5206e3eea73a37ad6cd">operations_research::pdlp::internal::DualTrustRegionProblem::NormWeight</a></div><div class="ttdeci">double NormWeight(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00405">trust_region.h:405</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html">operations_research::pdlp::internal::PrimalTrustRegionProblem</a></div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00342">trust_region.h:342</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem_html_a09ccf99be502491aacb4aa87583d2bdd"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a09ccf99be502491aacb4aa87583d2bdd">operations_research::pdlp::internal::PrimalTrustRegionProblem::Objective</a></div><div class="ttdeci">double Objective(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00352">trust_region.h:352</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem_html_a26c142eaecb81e4a80ac5cb5d7bfc1a3"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a26c142eaecb81e4a80ac5cb5d7bfc1a3">operations_research::pdlp::internal::PrimalTrustRegionProblem::UpperBound</a></div><div class="ttdeci">double UpperBound(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00356">trust_region.h:356</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem_html_a3a130beba19f9a43060251fc0b031330"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a3a130beba19f9a43060251fc0b031330">operations_research::pdlp::internal::PrimalTrustRegionProblem::LowerBound</a></div><div class="ttdeci">double LowerBound(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00353">trust_region.h:353</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem_html_a3cd894d3cf53f1e2e43070f945d08ef4"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a3cd894d3cf53f1e2e43070f945d08ef4">operations_research::pdlp::internal::PrimalTrustRegionProblem::PrimalTrustRegionProblem</a></div><div class="ttdeci">PrimalTrustRegionProblem(const QuadraticProgram *qp, const Eigen::VectorXd *primal_solution, const Eigen::VectorXd *primal_gradient, const double norm_weight=1.0)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00344">trust_region.h:344</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem_html_a745a6cbad664d808756705f7c7920754"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#a745a6cbad664d808756705f7c7920754">operations_research::pdlp::internal::PrimalTrustRegionProblem::CenterPoint</a></div><div class="ttdeci">double CenterPoint(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00359">trust_region.h:359</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem_html_adbf3f8e0abf2f5206e3eea73a37ad6cd"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1internal_1_1_primal_trust_region_problem.html#adbf3f8e0abf2f5206e3eea73a37ad6cd">operations_research::pdlp::internal::PrimalTrustRegionProblem::NormWeight</a></div><div class="ttdeci">double NormWeight(int64_t index) const</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00360">trust_region.h:360</a></div></div>
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<div class="ttc" id="acp__model__solver_8cc_html_a06dad0852d85b0686e01c084207c03a7"><div class="ttname"><a href="cp__model__solver_8cc.html#a06dad0852d85b0686e01c084207c03a7">bounds</a></div><div class="ttdeci">SharedBoundsManager * bounds</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__solver_8cc_source.html#l02051">cp_model_solver.cc:2051</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="amathutil_8h_html"><div class="ttname"><a href="mathutil_8h.html">mathutil.h</a></div></div>
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<div class="ttc" id="anamespaceinternal_html"><div class="ttname"><a href="namespaceinternal.html">internal</a></div><div class="ttdef"><b>Definition:</b> <a href="connected__components_8h_source.html#l00138">connected_components.h:138</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_a89e736fe381fad1600024fa36345650b"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#a89e736fe381fad1600024fa36345650b">operations_research::pdlp::internal::DistanceAtCriticalStepSize</a></div><div class="ttdeci">double DistanceAtCriticalStepSize(const TrustRegionProblem &problem, const int64_t index)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00189">trust_region.h:189</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_1_1internal_html_a8cbe1743f36aed0a68c446f0392ec93c"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#a8cbe1743f36aed0a68c446f0392ec93c">operations_research::pdlp::internal::CriticalStepSize</a></div><div class="ttdeci">double CriticalStepSize(const TrustRegionProblem &problem, const int64_t index)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00204">trust_region.h:204</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_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_a39f9a12aa1bd94ddb3a56816d4d25eb0a974f1270f89b99d15b58a4d35c26aedc"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a39f9a12aa1bd94ddb3a56816d4d25eb0a974f1270f89b99d15b58a4d35c26aedc">operations_research::pdlp::PrimalDualNorm::kMaxNorm</a></div><div class="ttdeci">@ kMaxNorm</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a39f9a12aa1bd94ddb3a56816d4d25eb0aaafbdb17e2f1da89be62331fa0cf5503"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a39f9a12aa1bd94ddb3a56816d4d25eb0aaafbdb17e2f1da89be62331fa0cf5503">operations_research::pdlp::PrimalDualNorm::kEuclideanNorm</a></div><div class="ttdeci">@ kEuclideanNorm</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_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_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_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_1pdlp_html_afdd1506c32f697aeb13c4b9a9f05ba03"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#afdd1506c32f697aeb13c4b9a9f05ba03">operations_research::pdlp::BoundGap</a></div><div class="ttdeci">double BoundGap(const LocalizedLagrangianBounds &bounds)</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00113">trust_region.h:113</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_localized_lagrangian_bounds_html_a1ba5ca0f61f2fa13bd23bf0f89004f35"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">operations_research::pdlp::LocalizedLagrangianBounds::upper_bound</a></div><div class="ttdeci">double upper_bound</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00108">trust_region.h:108</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds_html_a1e2f9a2352c1d9a6cada9544898fceec"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a1e2f9a2352c1d9a6cada9544898fceec">operations_research::pdlp::LocalizedLagrangianBounds::lower_bound</a></div><div class="ttdeci">double lower_bound</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00106">trust_region.h:106</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds_html_a3f67c53b80389c5f53961936edba04c9"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#a3f67c53b80389c5f53961936edba04c9">operations_research::pdlp::LocalizedLagrangianBounds::radius</a></div><div class="ttdeci">double radius</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00110">trust_region.h:110</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds_html_ad16c3e3b8e83fc9a72f8309bc63534b2"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_localized_lagrangian_bounds.html#ad16c3e3b8e83fc9a72f8309bc63534b2">operations_research::pdlp::LocalizedLagrangianBounds::lagrangian_value</a></div><div class="ttdeci">double lagrangian_value</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00104">trust_region.h:104</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_a097d329b7af662bea9b5a8e310a22726"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a097d329b7af662bea9b5a8e310a22726">operations_research::pdlp::QuadraticProgram::variable_upper_bounds</a></div><div class="ttdeci">Eigen::VectorXd variable_upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00133">quadratic_program.h:133</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_a0f72e7b49f91d0b980f5a54a18c06964"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">operations_research::pdlp::QuadraticProgram::variable_lower_bounds</a></div><div class="ttdeci">Eigen::VectorXd variable_lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00133">quadratic_program.h:133</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_a61349a88b7e83784a92be3d231cfa638"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">operations_research::pdlp::QuadraticProgram::constraint_lower_bounds</a></div><div class="ttdeci">Eigen::VectorXd constraint_lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00132">quadratic_program.h:132</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_af2acc3fce9196f0cd70ed7505923234c"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">operations_research::pdlp::QuadraticProgram::constraint_upper_bounds</a></div><div class="ttdeci">Eigen::VectorXd constraint_upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00132">quadratic_program.h:132</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_a69703b8569462134ad4e22ab0133e418"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_trust_region_result.html#a69703b8569462134ad4e22ab0133e418">operations_research::pdlp::TrustRegionResult::objective_value</a></div><div class="ttdeci">double objective_value</div><div class="ttdef"><b>Definition:</b> <a href="trust__region_8h_source.html#l00043">trust_region.h:43</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__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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