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<a href="solution_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>
<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 &quot;License&quot;);</span></div>
<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>
<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>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<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>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
<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>
<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 &quot;AS IS&quot; BASIS,</span></div>
<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>
<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>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#ifndef OR_TOOLS_MATH_OPT_CPP_SOLUTION_H_</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define OR_TOOLS_MATH_OPT_CPP_SOLUTION_H_</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;optional&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &quot;absl/types/optional.h&quot;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &quot;absl/types/span.h&quot;</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include &quot;<a class="code" href="model__storage_8h.html">ortools/math_opt/core/model_storage.h</a>&quot;</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include &quot;<a class="code" href="enums_8h.html">ortools/math_opt/cpp/enums.h</a>&quot;</span> <span class="comment">// IWYU pragma: export</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include &quot;<a class="code" href="math__opt_2cpp_2linear__constraint_8h.html">ortools/math_opt/cpp/linear_constraint.h</a>&quot;</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include &quot;<a class="code" href="variable__and__expressions_8h.html">ortools/math_opt/cpp/variable_and_expressions.h</a>&quot;</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include &quot;ortools/math_opt/result.pb.h&quot;</span> <span class="comment">// IWYU pragma: export</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include &quot;ortools/math_opt/solution.pb.h&quot;</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
<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_1math__opt.html">math_opt</a> {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// Feasibility of a primal or dual solution as claimed by the solver.</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3b"> 33</a></span><span class="keyword">enum class</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3b">SolutionStatus</a> {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// Solver does not claim a feasibility status.</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3ba180f453eb66237810dfc39ee46e04c9a">kUndetermined</a> = SOLUTION_STATUS_UNDETERMINED,</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// Solver claims the solution is feasible.</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3ba6936fc811b6bf3bfd7c65ab1f48e3f1f">kFeasible</a> = SOLUTION_STATUS_FEASIBLE,</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// Solver claims the solution is infeasible.</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <a class="code hl_enumvalue" href="namespaceoperations__research.html#aa17b6104527f45be5034e00d3c14249faa4d66aafc8bcba36b995fd8be0483574">kInfeasible</a> = SOLUTION_STATUS_INFEASIBLE,</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span>};</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1math__opt.html#a16d94c5f9a823b7b1ed2465bef57efeb"> 44</a></span><a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a6539b726794dda80e1570435b74b96f8">MATH_OPT_DEFINE_ENUM</a>(<a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3b">SolutionStatus</a>, SOLUTION_STATUS_UNSPECIFIED);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// Status of a variable/constraint in a LP basis.</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684"> 47</a></span><span class="keyword">enum class</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684">BasisStatus</a> : int8_t {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// The variable/constraint is free (it has no finite bounds).</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684a76c93a75b7476862edaf5f341c7f0aa6">kFree</a> = BASIS_STATUS_FREE,</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// The variable/constraint is at its lower bound (which must be finite).</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684a76e3c262bc5823ae6f807cf8670f4e4e">kAtLowerBound</a> = BASIS_STATUS_AT_LOWER_BOUND,</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// The variable/constraint is at its upper bound (which must be finite).</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684aa430e80aaabebd212623b7951d4fd376">kAtUpperBound</a> = BASIS_STATUS_AT_UPPER_BOUND,</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// The variable/constraint has identical finite lower and upper bounds.</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684a054895717e450c549ffa5d887b32f674">kFixedValue</a> = BASIS_STATUS_FIXED_VALUE,</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// The variable/constraint is basic.</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684a27296922b87cce1a26d3d54419a74599">kBasic</a> = BASIS_STATUS_BASIC,</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span>};</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1math__opt.html#aeeaaf9001d3c076add90e44d5047a878"> 64</a></span><a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a6539b726794dda80e1570435b74b96f8">MATH_OPT_DEFINE_ENUM</a>(<a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684">BasisStatus</a>, BASIS_STATUS_UNSPECIFIED);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">// A solution to an optimization problem.</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">//</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">// E.g. consider a simple linear program:</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment">// min c * x</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment">// s.t. A * x &gt;= b</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="comment">// x &gt;= 0.</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="comment">// A primal solution is assignment values to x. It is feasible if it satisfies</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment">// A * x &gt;= b and x &gt;= 0 from above. In the class PrimalSolution,</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment">// variable_values is x and objective_value is c * x.</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment">//</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">// For the general case of a MathOpt optimization model, see</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">// go/mathopt-solutions for details.</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_primal_solution.html"> 78</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_primal_solution.html">PrimalSolution</a> {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keyword">static</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_primal_solution.html">PrimalSolution</a> <a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a02dac9725348d8680374d56c8cde1555">FromProto</a>(</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model_storage.html">ModelStorage</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">const</span> PrimalSolutionProto&amp; primal_solution_proto);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a217b557acea6edff9d4174403dc2f2ff"> 83</a></span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">VariableMap&lt;double&gt;</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a217b557acea6edff9d4174403dc2f2ff">variable_values</a>;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a69703b8569462134ad4e22ab0133e418"> 84</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a69703b8569462134ad4e22ab0133e418">objective_value</a> = 0.0;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a443e96aa0d4868702db56edfb93ff51f"> 86</a></span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3b">SolutionStatus</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a443e96aa0d4868702db56edfb93ff51f">feasibility_status</a> = <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3ba180f453eb66237810dfc39ee46e04c9a">SolutionStatus::kUndetermined</a>;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span>};</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment">// A direction of unbounded improvement to an optimization problem;</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="comment">// equivalently, a certificate of infeasibility for the dual of the</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="comment">// optimization problem.</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">//</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="comment">// E.g. consider a simple linear program:</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment">// min c * x</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment">// s.t. A * x &gt;= b</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment">// x &gt;= 0</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// A primal ray is an x that satisfies:</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// c * x &lt; 0</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment">// A * x &gt;= 0</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// x &gt;= 0</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment">// Observe that given a feasible solution, any positive multiple of the primal</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment">// ray plus that solution is still feasible, and gives a better objective</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="comment">// value. A primal ray also proves the dual optimization problem infeasible.</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment">//</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="comment">// In the class PrimalRay, variable_values is this x.</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment">//</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment">// For the general case of a MathOpt optimization model, see</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment">// go/mathopt-solutions for details.</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_primal_ray.html"> 109</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_primal_ray.html">PrimalRay</a> {</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">static</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_primal_ray.html">PrimalRay</a> <a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_primal_ray.html#a9bd9a013c3c2599d08dc2b8283babb84">FromProto</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model_storage.html">ModelStorage</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">const</span> PrimalRayProto&amp; primal_ray_proto);</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_primal_ray.html#a217b557acea6edff9d4174403dc2f2ff"> 113</a></span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">VariableMap&lt;double&gt;</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_primal_ray.html#a217b557acea6edff9d4174403dc2f2ff">variable_values</a>;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span>};</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="comment">// A solution to the dual of an optimization problem.</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">//</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment">// E.g. consider the primal dual pair linear program pair:</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment">// (Primal) (Dual)</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment">// min c * x max b * y</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment">// s.t. A * x &gt;= b s.t. y * A + r = c</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="comment">// x &gt;= 0 y, r &gt;= 0.</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="comment">// The dual solution is the pair (y, r). It is feasible if it satisfies the</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment">// constraints from (Dual) above.</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span><span class="comment">//</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="comment">// Below, y is dual_values, r is reduced_costs, and b * y is objective value.</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="comment">//</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><span class="comment">// For the general case, see go/mathopt-solutions and go/mathopt-dual (and</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="comment">// note that the dual objective depends on r in the general case).</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_dual_solution.html"> 130</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_dual_solution.html">DualSolution</a> {</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keyword">static</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_dual_solution.html">DualSolution</a> <a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a5b7efc521747cedfacf0d196e5123d3d">FromProto</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model_storage.html">ModelStorage</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keyword">const</span> DualSolutionProto&amp; dual_solution_proto);</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a801b3639c3daff80850bf450a95fab3d"> 134</a></span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">LinearConstraintMap&lt;double&gt;</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a801b3639c3daff80850bf450a95fab3d">dual_values</a>;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a8c59e260c5341833e0c29dfbeb4b92a3"> 135</a></span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">VariableMap&lt;double&gt;</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a8c59e260c5341833e0c29dfbeb4b92a3">reduced_costs</a>;</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#abc4831916e7e8dc12c4009f5c720a301"> 136</a></span> std::optional&lt;double&gt; <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#abc4831916e7e8dc12c4009f5c720a301">objective_value</a>;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> </div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a443e96aa0d4868702db56edfb93ff51f"> 138</a></span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3b">SolutionStatus</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a443e96aa0d4868702db56edfb93ff51f">feasibility_status</a> = <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3ba180f453eb66237810dfc39ee46e04c9a">SolutionStatus::kUndetermined</a>;</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span>};</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment">// A direction of unbounded improvement to the dual of an optimization,</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment">// problem; equivalently, a certificate of primal infeasibility.</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment">//</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="comment">// E.g. consider the primal dual pair linear program pair:</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="comment">// (Primal) (Dual)</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span><span class="comment">// min c * x max b * y</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="comment">// s.t. A * x &gt;= b s.t. y * A + r = c</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="comment">// x &gt;= 0 y, r &gt;= 0.</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="comment">// The dual ray is the pair (y, r) satisfying:</span></div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="comment">// b * y &gt; 0</span></div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="comment">// y * A + r = 0</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="comment">// y, r &gt;= 0</span></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span><span class="comment">// Observe that adding a positive multiple of (y, r) to dual feasible solution</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="comment">// maintains dual feasibility and improves the objective (proving the dual is</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="comment">// unbounded). The dual ray also proves the primal problem is infeasible.</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="comment">//</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="comment">// In the class DualRay, y is dual_values and r is reduced_costs.</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span><span class="comment">//</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="comment">// For the general case, see go/mathopt-solutions and go/mathopt-dual (and</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="comment">// note that the dual objective depends on r in the general case).</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_dual_ray.html"> 161</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_dual_ray.html">DualRay</a> {</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keyword">static</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_dual_ray.html">DualRay</a> <a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_dual_ray.html#acda5b63c466a90aec580c4509165bfaf">FromProto</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model_storage.html">ModelStorage</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="keyword">const</span> DualRayProto&amp; dual_ray_proto);</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_dual_ray.html#a801b3639c3daff80850bf450a95fab3d"> 165</a></span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">LinearConstraintMap&lt;double&gt;</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_dual_ray.html#a801b3639c3daff80850bf450a95fab3d">dual_values</a>;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_dual_ray.html#a8c59e260c5341833e0c29dfbeb4b92a3"> 166</a></span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">VariableMap&lt;double&gt;</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_dual_ray.html#a8c59e260c5341833e0c29dfbeb4b92a3">reduced_costs</a>;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span>};</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="comment">// A combinatorial characterization for a solution to a linear program.</span></div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="comment">//</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="comment">// The simplex method for solving linear programs always returns a &quot;basic</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="comment">// feasible solution&quot; which can be described combinatorially as a Basis. A</span></div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="comment">// basis assigns a BasisStatus for every variable and linear constraint.</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="comment">//</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span><span class="comment">// E.g. consider a standard form LP:</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span><span class="comment">// min c * x</span></div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="comment">// s.t. A * x = b</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span><span class="comment">// x &gt;= 0</span></div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span><span class="comment">// that has more variables than constraints and with full row rank A.</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span><span class="comment">//</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span><span class="comment">// Let n be the number of variables and m the number of linear constraints. A</span></div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span><span class="comment">// valid basis for this problem can be constructed as follows:</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span><span class="comment">// * All constraints will have basis status FIXED.</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span><span class="comment">// * Pick m variables such that the columns of A are linearly independent and</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span><span class="comment">// assign the status BASIC.</span></div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span><span class="comment">// * Assign the status AT_LOWER for the remaining n - m variables.</span></div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span><span class="comment">//</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="comment">// The basic solution for this basis is the unique solution of A * x = b that</span></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span><span class="comment">// has all variables with status AT_LOWER fixed to their lower bounds (all</span></div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span><span class="comment">// zero). The resulting solution is called a basic feasible solution if it</span></div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span><span class="comment">// also satisfies x &gt;= 0.</span></div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span><span class="comment">//</span></div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span><span class="comment">// See go/mathopt-basis for treatment of the general case and an explanation</span></div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span><span class="comment">// of how a dual solution is determined for a basis.</span></div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_basis.html"> 195</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_basis.html">Basis</a> {</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="comment">// Returns a Basis built from the input indexed_basis, CHECKing that no</span></div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="comment">// values is BASIS_STATUS_UNSPECIFIED. No check is done on other values so</span></div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// out of bounds values e.g. BasisStatusProto_MAX+1 won&#39;t raise an</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// assertion. See SpaseBasisStatusVectorIsValid().</span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keyword">static</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_basis.html">Basis</a> <a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_basis.html#aceff2f0b4321364c4ad77ff064ec422b">FromProto</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model_storage.html">ModelStorage</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keyword">const</span> BasisProto&amp; basis_proto);</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> </div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_basis.html#a861aab8e91d4e8a0201d4de3154cf01f"> 203</a></span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">LinearConstraintMap&lt;BasisStatus&gt;</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_basis.html#a861aab8e91d4e8a0201d4de3154cf01f">constraint_status</a>;</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_basis.html#a5dc49f0eb9f9a7a1f0d1a0e93a823bc5"> 204</a></span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">VariableMap&lt;BasisStatus&gt;</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_basis.html#a5dc49f0eb9f9a7a1f0d1a0e93a823bc5">variable_status</a>;</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// This is an advanced status. For single-sided LPs it should be equal to the</span></div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// feasibility status of the associated dual solution. For two-sided LPs it</span></div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// may be different in some edge cases (e.g. incomplete solves with primal</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// simplex). For more details see go/mathopt-basis-advanced#dualfeasibility.</span></div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_basis.html#ae445af2dc4f84f6c44a4a66978c700dc"> 210</a></span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3b">SolutionStatus</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_basis.html#ae445af2dc4f84f6c44a4a66978c700dc">basic_dual_feasibility</a> = <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3ba180f453eb66237810dfc39ee46e04c9a">SolutionStatus::kUndetermined</a>;</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span>};</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span><span class="comment">// What is included in a solution depends on the kind of problem and solver.</span></div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span><span class="comment">// The current common patterns are</span></div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span><span class="comment">// 1. MIP solvers return only a primal solution.</span></div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span><span class="comment">// 2. Simplex LP solvers often return a basis and the primal and dual</span></div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span><span class="comment">// solutions associated to this basis.</span></div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span><span class="comment">// 3. Other continuous solvers often return a primal and dual solution</span></div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span><span class="comment">// solution that are connected in a solver-dependent form.</span></div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_solution.html"> 220</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solution.html">Solution</a> {</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keyword">static</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solution.html">Solution</a> <a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solution.html#a3f051d41c35cca832372a5658528e13c">FromProto</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model_storage.html">ModelStorage</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keyword">const</span> SolutionProto&amp; solution_proto);</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_solution.html#aed349b94d0cb57c4bfe7ca7fa25391ef"> 223</a></span> std::optional&lt;PrimalSolution&gt; <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solution.html#aed349b94d0cb57c4bfe7ca7fa25391ef">primal_solution</a>;</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_solution.html#ade7f0087f8705aedf57e55eef0566c2d"> 224</a></span> std::optional&lt;DualSolution&gt; <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solution.html#ade7f0087f8705aedf57e55eef0566c2d">dual_solution</a>;</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_solution.html#af147118ba6bbf5e4f3284359cf2c0710"> 225</a></span> std::optional&lt;Basis&gt; <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solution.html#af147118ba6bbf5e4f3284359cf2c0710">basis</a>;</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span>};</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> </div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span>} <span class="comment">// namespace math_opt</span></div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span>} <span class="comment">// namespace operations_research</span></div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> </div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_MATH_OPT_CPP_SOLUTION_H_</span></div>
<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_id_map_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_id_map.html">operations_research::math_opt::IdMap</a></div><div class="ttdef"><b>Definition:</b> <a href="id__map_8h_source.html#l00053">id_map.h:53</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_model_storage_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_model_storage.html">operations_research::math_opt::ModelStorage</a></div><div class="ttdef"><b>Definition:</b> <a href="model__storage_8h_source.html#l00155">model_storage.h:155</a></div></div>
<div class="ttc" id="aenums_8h_html"><div class="ttname"><a href="enums_8h.html">enums.h</a></div></div>
<div class="ttc" id="agurobi__interface_8cc_html_a0728f23c9a47655d38e0bf1a2f200bcf"><div class="ttname"><a href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a></div><div class="ttdeci">GRBmodel * model</div><div class="ttdef"><b>Definition:</b> <a href="gurobi__interface_8cc_source.html#l00274">gurobi_interface.cc:274</a></div></div>
<div class="ttc" id="amath__opt_2cpp_2linear__constraint_8h_html"><div class="ttname"><a href="math__opt_2cpp_2linear__constraint_8h.html">linear_constraint.h</a></div></div>
<div class="ttc" id="amodel__storage_8h_html"><div class="ttname"><a href="model__storage_8h.html">model_storage.h</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html">operations_research::math_opt</a></div><div class="ttdef"><b>Definition:</b> <a href="arrow__operator__proxy_8h_source.html#l00020">arrow_operator_proxy.h:20</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a5c12f31ca91b1412d51fd5fa6f82e684"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684">operations_research::math_opt::BasisStatus</a></div><div class="ttdeci">BasisStatus</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00047">solution.h:47</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a5c12f31ca91b1412d51fd5fa6f82e684a054895717e450c549ffa5d887b32f674"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684a054895717e450c549ffa5d887b32f674">operations_research::math_opt::BasisStatus::kFixedValue</a></div><div class="ttdeci">@ kFixedValue</div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a5c12f31ca91b1412d51fd5fa6f82e684a27296922b87cce1a26d3d54419a74599"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684a27296922b87cce1a26d3d54419a74599">operations_research::math_opt::BasisStatus::kBasic</a></div><div class="ttdeci">@ kBasic</div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a5c12f31ca91b1412d51fd5fa6f82e684a76c93a75b7476862edaf5f341c7f0aa6"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684a76c93a75b7476862edaf5f341c7f0aa6">operations_research::math_opt::BasisStatus::kFree</a></div><div class="ttdeci">@ kFree</div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a5c12f31ca91b1412d51fd5fa6f82e684a76e3c262bc5823ae6f807cf8670f4e4e"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684a76e3c262bc5823ae6f807cf8670f4e4e">operations_research::math_opt::BasisStatus::kAtLowerBound</a></div><div class="ttdeci">@ kAtLowerBound</div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a5c12f31ca91b1412d51fd5fa6f82e684aa430e80aaabebd212623b7951d4fd376"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a5c12f31ca91b1412d51fd5fa6f82e684aa430e80aaabebd212623b7951d4fd376">operations_research::math_opt::BasisStatus::kAtUpperBound</a></div><div class="ttdeci">@ kAtUpperBound</div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a6539b726794dda80e1570435b74b96f8"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a6539b726794dda80e1570435b74b96f8">operations_research::math_opt::MATH_OPT_DEFINE_ENUM</a></div><div class="ttdeci">MATH_OPT_DEFINE_ENUM(CallbackEvent, CALLBACK_EVENT_UNSPECIFIED)</div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a801be40a606301461ff812058569ee3b"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3b">operations_research::math_opt::SolutionStatus</a></div><div class="ttdeci">SolutionStatus</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00033">solution.h:33</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a801be40a606301461ff812058569ee3ba180f453eb66237810dfc39ee46e04c9a"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3ba180f453eb66237810dfc39ee46e04c9a">operations_research::math_opt::SolutionStatus::kUndetermined</a></div><div class="ttdeci">@ kUndetermined</div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a801be40a606301461ff812058569ee3ba6936fc811b6bf3bfd7c65ab1f48e3f1f"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a801be40a606301461ff812058569ee3ba6936fc811b6bf3bfd7c65ab1f48e3f1f">operations_research::math_opt::SolutionStatus::kFeasible</a></div><div class="ttdeci">@ kFeasible</div></div>
<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_aa17b6104527f45be5034e00d3c14249faa4d66aafc8bcba36b995fd8be0483574"><div class="ttname"><a href="namespaceoperations__research.html#aa17b6104527f45be5034e00d3c14249faa4d66aafc8bcba36b995fd8be0483574">operations_research::GScipHintResult::kInfeasible</a></div><div class="ttdeci">@ kInfeasible</div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_basis_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_basis.html">operations_research::math_opt::Basis</a></div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00195">solution.h:195</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_basis_html_a5dc49f0eb9f9a7a1f0d1a0e93a823bc5"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_basis.html#a5dc49f0eb9f9a7a1f0d1a0e93a823bc5">operations_research::math_opt::Basis::variable_status</a></div><div class="ttdeci">VariableMap&lt; BasisStatus &gt; variable_status</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00204">solution.h:204</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_basis_html_a861aab8e91d4e8a0201d4de3154cf01f"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_basis.html#a861aab8e91d4e8a0201d4de3154cf01f">operations_research::math_opt::Basis::constraint_status</a></div><div class="ttdeci">LinearConstraintMap&lt; BasisStatus &gt; constraint_status</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00203">solution.h:203</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_basis_html_aceff2f0b4321364c4ad77ff064ec422b"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_basis.html#aceff2f0b4321364c4ad77ff064ec422b">operations_research::math_opt::Basis::FromProto</a></div><div class="ttdeci">static Basis FromProto(const ModelStorage *model, const BasisProto &amp;basis_proto)</div><div class="ttdef"><b>Definition:</b> <a href="solution_8cc_source.html#l00159">solution.cc:159</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_basis_html_ae445af2dc4f84f6c44a4a66978c700dc"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_basis.html#ae445af2dc4f84f6c44a4a66978c700dc">operations_research::math_opt::Basis::basic_dual_feasibility</a></div><div class="ttdeci">SolutionStatus basic_dual_feasibility</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00210">solution.h:210</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_ray_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_ray.html">operations_research::math_opt::DualRay</a></div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00161">solution.h:161</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_ray_html_a801b3639c3daff80850bf450a95fab3d"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_ray.html#a801b3639c3daff80850bf450a95fab3d">operations_research::math_opt::DualRay::dual_values</a></div><div class="ttdeci">LinearConstraintMap&lt; double &gt; dual_values</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00165">solution.h:165</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_ray_html_a8c59e260c5341833e0c29dfbeb4b92a3"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_ray.html#a8c59e260c5341833e0c29dfbeb4b92a3">operations_research::math_opt::DualRay::reduced_costs</a></div><div class="ttdeci">VariableMap&lt; double &gt; reduced_costs</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00166">solution.h:166</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_ray_html_acda5b63c466a90aec580c4509165bfaf"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_ray.html#acda5b63c466a90aec580c4509165bfaf">operations_research::math_opt::DualRay::FromProto</a></div><div class="ttdeci">static DualRay FromProto(const ModelStorage *model, const DualRayProto &amp;dual_ray_proto)</div><div class="ttdef"><b>Definition:</b> <a href="solution_8cc_source.html#l00151">solution.cc:151</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_solution_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_solution.html">operations_research::math_opt::DualSolution</a></div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00130">solution.h:130</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_solution_html_a443e96aa0d4868702db56edfb93ff51f"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a443e96aa0d4868702db56edfb93ff51f">operations_research::math_opt::DualSolution::feasibility_status</a></div><div class="ttdeci">SolutionStatus feasibility_status</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00138">solution.h:138</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_solution_html_a5b7efc521747cedfacf0d196e5123d3d"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a5b7efc521747cedfacf0d196e5123d3d">operations_research::math_opt::DualSolution::FromProto</a></div><div class="ttdeci">static DualSolution FromProto(const ModelStorage *model, const DualSolutionProto &amp;dual_solution_proto)</div><div class="ttdef"><b>Definition:</b> <a href="solution_8cc_source.html#l00133">solution.cc:133</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_solution_html_a801b3639c3daff80850bf450a95fab3d"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a801b3639c3daff80850bf450a95fab3d">operations_research::math_opt::DualSolution::dual_values</a></div><div class="ttdeci">LinearConstraintMap&lt; double &gt; dual_values</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00134">solution.h:134</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_solution_html_a8c59e260c5341833e0c29dfbeb4b92a3"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_solution.html#a8c59e260c5341833e0c29dfbeb4b92a3">operations_research::math_opt::DualSolution::reduced_costs</a></div><div class="ttdeci">VariableMap&lt; double &gt; reduced_costs</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00135">solution.h:135</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_dual_solution_html_abc4831916e7e8dc12c4009f5c720a301"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_dual_solution.html#abc4831916e7e8dc12c4009f5c720a301">operations_research::math_opt::DualSolution::objective_value</a></div><div class="ttdeci">std::optional&lt; double &gt; objective_value</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00136">solution.h:136</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_primal_ray_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_primal_ray.html">operations_research::math_opt::PrimalRay</a></div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00109">solution.h:109</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_primal_ray_html_a217b557acea6edff9d4174403dc2f2ff"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_primal_ray.html#a217b557acea6edff9d4174403dc2f2ff">operations_research::math_opt::PrimalRay::variable_values</a></div><div class="ttdeci">VariableMap&lt; double &gt; variable_values</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00113">solution.h:113</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_primal_ray_html_a9bd9a013c3c2599d08dc2b8283babb84"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_primal_ray.html#a9bd9a013c3c2599d08dc2b8283babb84">operations_research::math_opt::PrimalRay::FromProto</a></div><div class="ttdeci">static PrimalRay FromProto(const ModelStorage *model, const PrimalRayProto &amp;primal_ray_proto)</div><div class="ttdef"><b>Definition:</b> <a href="solution_8cc_source.html#l00127">solution.cc:127</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_primal_solution_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_primal_solution.html">operations_research::math_opt::PrimalSolution</a></div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00078">solution.h:78</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_primal_solution_html_a02dac9725348d8680374d56c8cde1555"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a02dac9725348d8680374d56c8cde1555">operations_research::math_opt::PrimalSolution::FromProto</a></div><div class="ttdeci">static PrimalSolution FromProto(const ModelStorage *model, const PrimalSolutionProto &amp;primal_solution_proto)</div><div class="ttdef"><b>Definition:</b> <a href="solution_8cc_source.html#l00112">solution.cc:112</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_primal_solution_html_a217b557acea6edff9d4174403dc2f2ff"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a217b557acea6edff9d4174403dc2f2ff">operations_research::math_opt::PrimalSolution::variable_values</a></div><div class="ttdeci">VariableMap&lt; double &gt; variable_values</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00083">solution.h:83</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_primal_solution_html_a443e96aa0d4868702db56edfb93ff51f"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a443e96aa0d4868702db56edfb93ff51f">operations_research::math_opt::PrimalSolution::feasibility_status</a></div><div class="ttdeci">SolutionStatus feasibility_status</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00086">solution.h:86</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_primal_solution_html_a69703b8569462134ad4e22ab0133e418"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_primal_solution.html#a69703b8569462134ad4e22ab0133e418">operations_research::math_opt::PrimalSolution::objective_value</a></div><div class="ttdeci">double objective_value</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00084">solution.h:84</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solution_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solution.html">operations_research::math_opt::Solution</a></div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00220">solution.h:220</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solution_html_a3f051d41c35cca832372a5658528e13c"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solution.html#a3f051d41c35cca832372a5658528e13c">operations_research::math_opt::Solution::FromProto</a></div><div class="ttdeci">static Solution FromProto(const ModelStorage *model, const SolutionProto &amp;solution_proto)</div><div class="ttdef"><b>Definition:</b> <a href="solution_8cc_source.html#l00174">solution.cc:174</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solution_html_ade7f0087f8705aedf57e55eef0566c2d"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solution.html#ade7f0087f8705aedf57e55eef0566c2d">operations_research::math_opt::Solution::dual_solution</a></div><div class="ttdeci">std::optional&lt; DualSolution &gt; dual_solution</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00224">solution.h:224</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solution_html_aed349b94d0cb57c4bfe7ca7fa25391ef"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solution.html#aed349b94d0cb57c4bfe7ca7fa25391ef">operations_research::math_opt::Solution::primal_solution</a></div><div class="ttdeci">std::optional&lt; PrimalSolution &gt; primal_solution</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00223">solution.h:223</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solution_html_af147118ba6bbf5e4f3284359cf2c0710"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solution.html#af147118ba6bbf5e4f3284359cf2c0710">operations_research::math_opt::Solution::basis</a></div><div class="ttdeci">std::optional&lt; Basis &gt; basis</div><div class="ttdef"><b>Definition:</b> <a href="solution_8h_source.html#l00225">solution.h:225</a></div></div>
<div class="ttc" id="avariable__and__expressions_8h_html"><div class="ttname"><a href="variable__and__expressions_8h.html">variable_and_expressions.h</a></div></div>
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