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280 lines
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<div class="headertitle"><div class="title">primal_dual_hybrid_gradient.h</div></div>
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<a href="primal__dual__hybrid__gradient_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_PRIMAL_DUAL_HYBRID_GRADIENT_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_PRIMAL_DUAL_HYBRID_GRADIENT_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 <atomic></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <functional></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include "Eigen/Core"</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include "absl/status/statusor.h"</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include "absl/types/optional.h"</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "ortools/linear_solver/linear_solver.pb.h"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "<a class="code" href="lp__data_8h.html">ortools/lp_data/lp_data.h</a>"</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="quadratic__program_8h.html">ortools/pdlp/quadratic_program.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 "ortools/pdlp/solve_log.pb.h"</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include "ortools/pdlp/solvers.pb.h"</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="termination_8h.html">ortools/pdlp/termination.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_primal_and_dual_solution.html"> 32</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_primal_and_dual_solution.html">PrimalAndDualSolution</a> {</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_primal_and_dual_solution.html#aba446ee2bbf0217015660220ecf8d935"> 33</a></span> Eigen::VectorXd <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_primal_and_dual_solution.html#aba446ee2bbf0217015660220ecf8d935">primal_solution</a>;</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_primal_and_dual_solution.html#a7240a2ad18b5d152e29675e53bcd117d"> 34</a></span> Eigen::VectorXd <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_primal_and_dual_solution.html#a7240a2ad18b5d152e29675e53bcd117d">dual_solution</a>;</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span>};</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// The following table defines the interpretation of the result vectors</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// depending on the value of solve_log.termination_reason: (the</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// TERMINATION_REASON_ prefix is omitted for brevity):</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">//</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// * OPTIMAL: the vectors satisfy the termination criteria for optimality.</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// * PRIMAL_INFEASIBLE: dual_solution and reduced_costs provide an approximate</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// certificate of primal infeasibility; see</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// https://developers.google.com/optimization/lp/pdlp_math#infeasibility_identification</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// for more information.</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// * DUAL_INFEASIBLE: primal_solution provides an approximate certificate of</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// dual infeasibility; see</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// https://developers.google.com/optimization/lp/pdlp_math#infeasibility_identification</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// for more information.</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// * PRIMAL_OR_DUAL_INFEASIBLE: the problem was shown to be primal and/or dual</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// infeasible but no certificate of infeasibility is available. The</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// primal_solution and dual_solution have no meaning. This status is only used</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// when presolve is enabled.</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// * TIME_LIMIT, ITERATION_LIMIT, KKT_MATRIX_PASS_LIMIT, NUMERICAL_ERROR,</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">// INTERRUPTED_BY_USER: the vectors contain an iterate at the time that the</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// respective event occurred. Their values may or may not be meaningful. In</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment">// some cases solution quality information is available; see documentation for</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// solve_log.solution_type.</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">// * INVALID_PROBLEM, INVALID_PARAMETER, OTHER: the solution vectors are</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// meaningless and may not have lengths consistent with the input problem.</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_solver_result.html"> 61</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_solver_result.html">SolverResult</a> {</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_solver_result.html#aba446ee2bbf0217015660220ecf8d935"> 62</a></span> Eigen::VectorXd <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_solver_result.html#aba446ee2bbf0217015660220ecf8d935">primal_solution</a>;</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// See https://developers.google.com/optimization/lp/pdlp_math for the</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// interpretation of the dual and reduced costs.</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_solver_result.html#a7240a2ad18b5d152e29675e53bcd117d"> 65</a></span> Eigen::VectorXd <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_solver_result.html#a7240a2ad18b5d152e29675e53bcd117d">dual_solution</a>;</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_solver_result.html#a8d7bbc7423c1c9f57c94de234c72ae47"> 66</a></span> Eigen::VectorXd <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_solver_result.html#a8d7bbc7423c1c9f57c94de234c72ae47">reduced_costs</a>;</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_solver_result.html#a365551ee87d4c047b1a0a06eedc41faf"> 67</a></span> SolveLog <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_solver_result.html#a365551ee87d4c047b1a0a06eedc41faf">solve_log</a>;</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span>};</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html"> 70</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html">IterationCallbackInfo</a> {</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a9c22f6575c59f8d6806a0a72ec1595a6"> 71</a></span> TerminationCriteria <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a9c22f6575c59f8d6806a0a72ec1595a6">termination_criteria</a>;</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a672ca0a58b23205b89a615c507650004"> 72</a></span> IterationStats <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a672ca0a58b23205b89a615c507650004">iteration_stats</a>;</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"><a class="line" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a9d8e486ae7a7ba200df62368442ee4d0"> 73</a></span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program_bound_norms.html">QuadraticProgramBoundNorms</a> <a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a9d8e486ae7a7ba200df62368442ee4d0">bound_norms</a>;</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span>};</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">// Solves the given QP using PDLP (Primal-Dual hybrid gradient enhanced for LP).</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">//</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment">// All operations that are repeated each iteration are executed in parallel</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment">// using params.num_threads() threads.</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment">//</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="comment">// The algorithm generally follows the description in</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment">// https://arxiv.org/pdf/2106.04756.pdf, with further enhancements for QP.</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment">// Notation here and in the implementation follows Chambolle and Pock, "On the</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment">// ergodic convergence rates of a first-order primal-dual algorithm"</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment">// (http://www.optimization-online.org/DB_FILE/2014/09/4532.pdf).</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment">// That paper doesn't explicitly use the terminology "primal-dual hybrid</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment">// gradient" but their Theorem 1 is analyzing PDHG. See</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</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="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment">// for the saddle-point formulation of the QP we use that is compatible with</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="comment">// Chambolle and Pock.</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="comment">//</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">// We use 0.5 ||.||^2 for both the primal and dual distance functions.</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="comment">//</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment">// We parameterize the primal and dual step sizes (tau and sigma in Chambolle</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment">// and Pock) as:</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment">// primal_stepsize = step_size / primal_weight</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// dual_stepsize = step_size * primal_weight</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// where step_size and primal_weight are parameters.</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment">// params.linesearch_rule determines the update rule for step_size.</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// params.initial_primal_weight specifies how primal_weight is initialized</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment">// and params.primal_weight_update_smoothing controls how primal_weight is</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment">// updated.</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="comment">//</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment">// If interrupt_solve is not nullptr, then the solver will periodically check if</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="comment">// interrupt_solve->load() is true, in which case the solve will terminate with</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment">// TERMINATION_REASON_INTERRUPTED_BY_USER.</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment">//</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment">// If iteration_stats_callback is not nullptr, then at each termination step</span></div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="comment">// (when iteration stats are logged), iteration_stats_callback will also</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="comment">// be called with those iteration stats.</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="comment">//</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="comment">// Callers MUST check solve_log.termination_reason before using the vectors in</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span><span class="comment">// the SolverResult. See the comment on SolverResult for interpreting the</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="comment">// termination reason.</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span><span class="comment">//</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="comment">// All objective values reported by the algorithm are transformed by using</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">// QuadraticProgram::ApplyObjectiveScalingAndOffset.</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment">//</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment">// NOTE: qp is intentionally passed by value, because PrimalDualHybridGradient</span></div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment">// modifies its copy.</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a333f489ba459dad7b5491ec327d8340f"> 121</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_solver_result.html">SolverResult</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#ac43b4c39d3be5e0bced44530d50f8208">PrimalDualHybridGradient</a>(</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a> qp, <span class="keyword">const</span> PrimalDualHybridGradientParams& params,</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keyword">const</span> std::atomic<bool>* interrupt_solve = <span class="keyword">nullptr</span>,</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> std::function<<span class="keywordtype">void</span>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html">IterationCallbackInfo</a>&)> iteration_stats_callback =</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keyword">nullptr</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">// Like above but optionally starts with the given initial solution. If no</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><span class="comment">// initial solution is given the zero vector is used. In either case the initial</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="comment">// solution is projected onto the primal and dual variable bounds before use.</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="comment">// Convergence should be faster if the initial solution is close to an optimal</span></div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="comment">// solution. NOTE: initial_solution is intentionally passed by value.</span></div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#ab7135c4ca76ea167f2b17c74920e0f6f"> 132</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_solver_result.html">SolverResult</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#ac43b4c39d3be5e0bced44530d50f8208">PrimalDualHybridGradient</a>(</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a> qp, <span class="keyword">const</span> PrimalDualHybridGradientParams& params,</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> absl::optional<PrimalAndDualSolution> initial_solution,</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keyword">const</span> std::atomic<bool>* interrupt_solve = <span class="keyword">nullptr</span>,</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> std::function<<span class="keywordtype">void</span>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html">IterationCallbackInfo</a>&)> iteration_stats_callback =</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceinternal.html">internal</a> {</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment">// Computes variable and constraint statuses. This determines if primal</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment">// variables are at their bounds based on exact comparisons and therefore may</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment">// not work with unscaled solutions. The primal and dual solution in the</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="comment">// returned ProblemSolution are NOT set.</span></div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><a class="code hl_struct" href="structoperations__research_1_1glop_1_1_problem_solution.html">glop::ProblemSolution</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp_1_1internal.html#a3fe24e4dddd7460838c010f64fd3569a">ComputeStatuses</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="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_primal_and_dual_solution.html">PrimalAndDualSolution</a>& solution);</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> </div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span>} <span class="comment">// namespace internal</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span>} <span class="comment">// namespace operations_research::pdlp</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="preprocessor">#endif </span><span class="comment">// PDLP_PRIMAL_DUAL_HYBRID_GRADIENT_H_</span></div>
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<div class="ttc" id="alp__data_8h_html"><div class="ttname"><a href="lp__data_8h.html">lp_data.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_a3fe24e4dddd7460838c010f64fd3569a"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp_1_1internal.html#a3fe24e4dddd7460838c010f64fd3569a">operations_research::pdlp::internal::ComputeStatuses</a></div><div class="ttdeci">glop::ProblemSolution ComputeStatuses(const QuadraticProgram &qp, const PrimalAndDualSolution &solution)</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8cc_source.html#l01912">primal_dual_hybrid_gradient.cc:1912</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_ac43b4c39d3be5e0bced44530d50f8208"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#ac43b4c39d3be5e0bced44530d50f8208">operations_research::pdlp::PrimalDualHybridGradient</a></div><div class="ttdeci">SolverResult PrimalDualHybridGradient(QuadraticProgram qp, const PrimalDualHybridGradientParams &params, const std::atomic< bool > *interrupt_solve, IterationStatsCallback iteration_stats_callback)</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8cc_source.html#l01867">primal_dual_hybrid_gradient.cc:1867</a></div></div>
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<div class="ttc" id="aquadratic__program_8h_html"><div class="ttname"><a href="quadratic__program_8h.html">quadratic_program.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_problem_solution_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_problem_solution.html">operations_research::glop::ProblemSolution</a></div><div class="ttdef"><b>Definition:</b> <a href="lp__data_8h_source.html#l00660">lp_data.h:660</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_iteration_callback_info_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html">operations_research::pdlp::IterationCallbackInfo</a></div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00070">primal_dual_hybrid_gradient.h:70</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_iteration_callback_info_html_a672ca0a58b23205b89a615c507650004"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a672ca0a58b23205b89a615c507650004">operations_research::pdlp::IterationCallbackInfo::iteration_stats</a></div><div class="ttdeci">IterationStats iteration_stats</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00072">primal_dual_hybrid_gradient.h:72</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_iteration_callback_info_html_a9c22f6575c59f8d6806a0a72ec1595a6"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a9c22f6575c59f8d6806a0a72ec1595a6">operations_research::pdlp::IterationCallbackInfo::termination_criteria</a></div><div class="ttdeci">TerminationCriteria termination_criteria</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00071">primal_dual_hybrid_gradient.h:71</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_iteration_callback_info_html_a9d8e486ae7a7ba200df62368442ee4d0"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_iteration_callback_info.html#a9d8e486ae7a7ba200df62368442ee4d0">operations_research::pdlp::IterationCallbackInfo::bound_norms</a></div><div class="ttdeci">QuadraticProgramBoundNorms bound_norms</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00073">primal_dual_hybrid_gradient.h:73</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_primal_and_dual_solution_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_primal_and_dual_solution.html">operations_research::pdlp::PrimalAndDualSolution</a></div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00032">primal_dual_hybrid_gradient.h:32</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_primal_and_dual_solution_html_a7240a2ad18b5d152e29675e53bcd117d"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_primal_and_dual_solution.html#a7240a2ad18b5d152e29675e53bcd117d">operations_research::pdlp::PrimalAndDualSolution::dual_solution</a></div><div class="ttdeci">Eigen::VectorXd dual_solution</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00034">primal_dual_hybrid_gradient.h:34</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_primal_and_dual_solution_html_aba446ee2bbf0217015660220ecf8d935"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_primal_and_dual_solution.html#aba446ee2bbf0217015660220ecf8d935">operations_research::pdlp::PrimalAndDualSolution::primal_solution</a></div><div class="ttdeci">Eigen::VectorXd primal_solution</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00033">primal_dual_hybrid_gradient.h:33</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_bound_norms_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program_bound_norms.html">operations_research::pdlp::QuadraticProgramBoundNorms</a></div><div class="ttdef"><b>Definition:</b> <a href="termination_8h_source.html#l00030">termination.h:30</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_solver_result_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_solver_result.html">operations_research::pdlp::SolverResult</a></div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00061">primal_dual_hybrid_gradient.h:61</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_solver_result_html_a365551ee87d4c047b1a0a06eedc41faf"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_solver_result.html#a365551ee87d4c047b1a0a06eedc41faf">operations_research::pdlp::SolverResult::solve_log</a></div><div class="ttdeci">SolveLog solve_log</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00067">primal_dual_hybrid_gradient.h:67</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_solver_result_html_a7240a2ad18b5d152e29675e53bcd117d"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_solver_result.html#a7240a2ad18b5d152e29675e53bcd117d">operations_research::pdlp::SolverResult::dual_solution</a></div><div class="ttdeci">Eigen::VectorXd dual_solution</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00065">primal_dual_hybrid_gradient.h:65</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_solver_result_html_a8d7bbc7423c1c9f57c94de234c72ae47"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_solver_result.html#a8d7bbc7423c1c9f57c94de234c72ae47">operations_research::pdlp::SolverResult::reduced_costs</a></div><div class="ttdeci">Eigen::VectorXd reduced_costs</div><div class="ttdef"><b>Definition:</b> <a href="primal__dual__hybrid__gradient_8h_source.html#l00066">primal_dual_hybrid_gradient.h:66</a></div></div>
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