<ahref="lp__solver_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aname="l00001"></a><spanclass="lineno"> 1</span> <spanclass="comment">// Copyright 2010-2021 Google LLC</span></div>
<divclass="line"><aname="l00002"></a><spanclass="lineno"> 2</span> <spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
<divclass="line"><aname="l00003"></a><spanclass="lineno"> 3</span> <spanclass="comment">// you may not use this file except in compliance with the License.</span></div>
<divclass="line"><aname="l00004"></a><spanclass="lineno"> 4</span> <spanclass="comment">// You may obtain a copy of the License at</span></div>
<divclass="line"><aname="l00008"></a><spanclass="lineno"> 8</span> <spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<divclass="line"><aname="l00009"></a><spanclass="lineno"> 9</span> <spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
<divclass="line"><aname="l00010"></a><spanclass="lineno"> 10</span> <spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<divclass="line"><aname="l00011"></a><spanclass="lineno"> 11</span> <spanclass="comment">// See the License for the specific language governing permissions and</span></div>
<divclass="line"><aname="l00012"></a><spanclass="lineno"> 12</span> <spanclass="comment">// limitations under the License.</span></div>
<divclass="line"><aname="l00028"></a><spanclass="lineno"> 28</span> <spanclass="comment">// A full-fledged linear programming solver.</span></div>
<divclass="line"><aname="l00033"></a><spanclass="lineno"> 33</span> <spanclass="comment">// Sets and gets the solver parameters.</span></div>
<divclass="line"><aname="l00034"></a><spanclass="lineno"> 34</span> <spanclass="comment">// See the proto for an extensive documentation.</span></div>
<divclass="line"><aname="l00039"></a><spanclass="lineno"> 39</span> <spanclass="comment">// Solves the given linear program and returns the solve status. See the</span></div>
<divclass="line"><aname="l00040"></a><spanclass="lineno"> 40</span> <spanclass="comment">// ProblemStatus documentation for a description of the different values.</span></div>
<divclass="line"><aname="l00042"></a><spanclass="lineno"> 42</span> <spanclass="comment">// The solution can be retrieved afterwards using the getter functions below.</span></div>
<divclass="line"><aname="l00043"></a><spanclass="lineno"> 43</span> <spanclass="comment">// Note that depending on the returned ProblemStatus the solution values may</span></div>
<divclass="line"><aname="l00044"></a><spanclass="lineno"> 44</span> <spanclass="comment">// not mean much, so it is important to check the returned status.</span></div>
<divclass="line"><aname="l00046"></a><spanclass="lineno"> 46</span> <spanclass="comment">// Incrementality: From one Solve() call to the next, the internal state is</span></div>
<divclass="line"><aname="l00047"></a><spanclass="lineno"> 47</span> <spanclass="comment">// not cleared and the solver may take advantage of its current state if the</span></div>
<divclass="line"><aname="l00048"></a><spanclass="lineno"> 48</span> <spanclass="comment">// given lp is only slightly modified. If the modification is too important,</span></div>
<divclass="line"><aname="l00049"></a><spanclass="lineno"> 49</span> <spanclass="comment">// or if the solver does not see how to reuse the previous state efficiently,</span></div>
<divclass="line"><aname="l00050"></a><spanclass="lineno"> 50</span> <spanclass="comment">// it will just solve the problem from scratch. On the other hand, if the lp</span></div>
<divclass="line"><aname="l00051"></a><spanclass="lineno"> 51</span> <spanclass="comment">// is the same, calling Solve() again should basically resume the solve from</span></div>
<divclass="line"><aname="l00052"></a><spanclass="lineno"> 52</span> <spanclass="comment">// the last position. To disable this behavior, simply call Clear() before.</span></div>
<divclass="line"><aname="l00055"></a><spanclass="lineno"> 55</span> <spanclass="comment">// Same as Solve() but use the given time limit rather than constructing a new</span></div>
<divclass="line"><aname="l00056"></a><spanclass="lineno"> 56</span> <spanclass="comment">// one from the current GlopParameters.</span></div>
<divclass="line"><aname="l00062"></a><spanclass="lineno"> 62</span> <spanclass="comment">// Calling Solve() for the first time, or calling Clear() then Solve() on the</span></div>
<divclass="line"><aname="l00063"></a><spanclass="lineno"> 63</span> <spanclass="comment">// same problem is guaranted to be deterministic and to always give the same</span></div>
<divclass="line"><aname="l00064"></a><spanclass="lineno"> 64</span> <spanclass="comment">// result, assuming that no time limit was specified.</span></div>
<divclass="line"><aname="l00067"></a><spanclass="lineno"> 67</span> <spanclass="comment">// Advanced usage. This should be called before calling Solve(). It will</span></div>
<divclass="line"><aname="l00068"></a><spanclass="lineno"> 68</span> <spanclass="comment">// configure the solver to try to start from the given point for the next</span></div>
<divclass="line"><aname="l00069"></a><spanclass="lineno"> 69</span> <spanclass="comment">// Solve() only. Note that calling Clear() will invalidate this information.</span></div>
<divclass="line"><aname="l00071"></a><spanclass="lineno"> 71</span> <spanclass="comment">// If the set of variables/constraints with a BASIC status does not form a</span></div>
<divclass="line"><aname="l00072"></a><spanclass="lineno"> 72</span> <spanclass="comment">// basis a warning will be logged and the code will ignore it. Otherwise, the</span></div>
<divclass="line"><aname="l00073"></a><spanclass="lineno"> 73</span> <spanclass="comment">// non-basic variables will be initialized to their given status and solving</span></div>
<divclass="line"><aname="l00074"></a><spanclass="lineno"> 74</span> <spanclass="comment">// will start from there (even if the solution is not primal/dual feasible).</span></div>
<divclass="line"><aname="l00076"></a><spanclass="lineno"> 76</span> <spanclass="comment">// Important: There is no facility to transform this information in sync with</span></div>
<divclass="line"><aname="l00077"></a><spanclass="lineno"> 77</span> <spanclass="comment">// presolve. So you should probably disable presolve when using this since</span></div>
<divclass="line"><aname="l00078"></a><spanclass="lineno"> 78</span> <spanclass="comment">// otherwise there is a good chance that the matrix will change and that the</span></div>
<divclass="line"><aname="l00079"></a><spanclass="lineno"> 79</span> <spanclass="comment">// given basis will make no sense. Even worse if it happens to be factorizable</span></div>
<divclass="line"><aname="l00080"></a><spanclass="lineno"> 80</span> <spanclass="comment">// but doesn't correspond to what was intended.</span></div>
<divclass="line"><aname="l00084"></a><spanclass="lineno"> 84</span> <spanclass="comment">// This loads a given solution and computes related quantities so that the</span></div>
<divclass="line"><aname="l00085"></a><spanclass="lineno"> 85</span> <spanclass="comment">// getters below will refer to it.</span></div>
<divclass="line"><aname="l00087"></a><spanclass="lineno"> 87</span> <spanclass="comment">// Depending on the given solution status, this also checks the solution</span></div>
<divclass="line"><aname="l00088"></a><spanclass="lineno"> 88</span> <spanclass="comment">// feasibility or optimality. The exact behavior and tolerances are controlled</span></div>
<divclass="line"><aname="l00089"></a><spanclass="lineno"> 89</span> <spanclass="comment">// by the solver parameters. Because of this, the returned ProblemStatus may</span></div>
<divclass="line"><aname="l00090"></a><spanclass="lineno"> 90</span> <spanclass="comment">// be changed from the one passed in the ProblemSolution to ABNORMAL or</span></div>
<divclass="line"><aname="l00091"></a><spanclass="lineno"> 91</span> <spanclass="comment">// IMPRECISE. Note that this is the same logic as the one used by Solve() to</span></div>
<divclass="line"><aname="l00092"></a><spanclass="lineno"> 92</span> <spanclass="comment">// verify the solver solution.</span></div>
<divclass="line"><aname="l00096"></a><spanclass="lineno"> 96</span> <spanclass="comment">// Returns the objective value of the solution with its offset and scaling.</span></div>
<divclass="line"><aname="l00099"></a><spanclass="lineno"> 99</span> <spanclass="comment">// Accessors to information related to variables.</span></div>
<divclass="line"><aname="l00106"></a><spanclass="lineno"> 106</span> <spanclass="comment">// Accessors to information related to constraints. The activity of a</span></div>
<divclass="line"><aname="l00107"></a><spanclass="lineno"> 107</span> <spanclass="comment">// constraint is the sum of its linear terms evaluated with variables taking</span></div>
<divclass="line"><aname="l00108"></a><spanclass="lineno"> 108</span> <spanclass="comment">// their values at the current solution.</span></div>
<divclass="line"><aname="l00110"></a><spanclass="lineno"> 110</span> <spanclass="comment">// Note that the dual_values() do not take into account an eventual objective</span></div>
<divclass="line"><aname="l00111"></a><spanclass="lineno"> 111</span> <spanclass="comment">// scaling of the solved LinearProgram.</span></div>
<divclass="line"><aname="l00120"></a><spanclass="lineno"> 120</span> <spanclass="comment">// Returns the primal maximum infeasibility of the solution.</span></div>
<divclass="line"><aname="l00121"></a><spanclass="lineno"> 121</span> <spanclass="comment">// This indicates by how much the variable and constraint bounds are violated.</span></div>
<divclass="line"><aname="l00124"></a><spanclass="lineno"> 124</span> <spanclass="comment">// Returns the dual maximum infeasibility of the solution.</span></div>
<divclass="line"><aname="l00125"></a><spanclass="lineno"> 125</span> <spanclass="comment">// This indicates by how much the variable costs (i.e. objective) should be</span></div>
<divclass="line"><aname="l00126"></a><spanclass="lineno"> 126</span> <spanclass="comment">// modified for the solution to be an exact optimal solution.</span></div>
<divclass="line"><aname="l00129"></a><spanclass="lineno"> 129</span> <spanclass="comment">// Returns true if the solution status was OPTIMAL and it seems that there is</span></div>
<divclass="line"><aname="l00130"></a><spanclass="lineno"> 130</span> <spanclass="comment">// more than one basic optimal solution. Note that this solver always returns</span></div>
<divclass="line"><aname="l00131"></a><spanclass="lineno"> 131</span> <spanclass="comment">// an optimal BASIC solution and that there is only a finite number of them.</span></div>
<divclass="line"><aname="l00132"></a><spanclass="lineno"> 132</span> <spanclass="comment">// Moreover, given one basic solution, since the basis is always refactorized</span></div>
<divclass="line"><aname="l00133"></a><spanclass="lineno"> 133</span> <spanclass="comment">// at optimality before reporting the numerical result, then all the</span></div>
<divclass="line"><aname="l00134"></a><spanclass="lineno"> 134</span> <spanclass="comment">// quantities (even the floating point ones) should be always the same.</span></div>
<divclass="line"><aname="l00136"></a><spanclass="lineno"> 136</span> <spanclass="comment">// TODO(user): Test this behavior extensively if a client relies on it.</span></div>
<divclass="line"><aname="l00139"></a><spanclass="lineno"> 139</span> <spanclass="comment">// Returns the number of simplex iterations used by the last Solve().</span></div>
<divclass="line"><aname="l00142"></a><spanclass="lineno"> 142</span> <spanclass="comment">// Returns the "deterministic time" since the creation of the solver. Note</span></div>
<divclass="line"><aname="l00143"></a><spanclass="lineno"> 143</span> <spanclass="comment">// That this time is only increased when some operations take place in this</span></div>
<divclass="line"><aname="l00146"></a><spanclass="lineno"> 146</span> <spanclass="comment">// TODO(user): Currently, this is only modified when the simplex code is</span></div>
<divclass="line"><aname="l00149"></a><spanclass="lineno"> 149</span> <spanclass="comment">// TODO(user): Improve the correlation with the running time.</span></div>
<divclass="line"><aname="l00153"></a><spanclass="lineno"> 153</span> <spanclass="comment">// Resizes all the solution vectors to the given sizes.</span></div>
<divclass="line"><aname="l00154"></a><spanclass="lineno"> 154</span> <spanclass="comment">// This is used in case of error to make sure all the getter functions will</span></div>
<divclass="line"><aname="l00155"></a><spanclass="lineno"> 155</span> <spanclass="comment">// not crash when given row/col inside the initial linear program dimension.</span></div>
<divclass="line"><aname="l00158"></a><spanclass="lineno"> 158</span> <spanclass="comment">// Make sure the primal and dual values are within their bounds in order to</span></div>
<divclass="line"><aname="l00159"></a><spanclass="lineno"> 159</span> <spanclass="comment">// have a strong guarantee on the optimal solution. See</span></div>
<divclass="line"><aname="l00160"></a><spanclass="lineno"> 160</span> <spanclass="comment">// provide_strong_optimal_guarantee in the GlopParameters proto.</span></div>
<divclass="line"><aname="l00164"></a><spanclass="lineno"> 164</span> <spanclass="comment">// Runs the revised simplex algorithm if needed (i.e. if the program was not</span></div>
<divclass="line"><aname="l00165"></a><spanclass="lineno"> 165</span> <spanclass="comment">// already solved by the preprocessors).</span></div>
<divclass="line"><aname="l00169"></a><spanclass="lineno"> 169</span> <spanclass="comment">// Checks that the returned solution values and statuses are consistent.</span></div>
<divclass="line"><aname="l00170"></a><spanclass="lineno"> 170</span> <spanclass="comment">// Returns true if this is the case. See the code for the exact check</span></div>
<divclass="line"><aname="l00175"></a><spanclass="lineno"> 175</span> <spanclass="comment">// Returns true if there may be multiple optimal solutions.</span></div>
<divclass="line"><aname="l00176"></a><spanclass="lineno"> 176</span> <spanclass="comment">// The return value is true if:</span></div>
<divclass="line"><aname="l00177"></a><spanclass="lineno"> 177</span> <spanclass="comment">// - a non-fixed variable, at one of its boumds, has its reduced</span></div>
<divclass="line"><aname="l00178"></a><spanclass="lineno"> 178</span> <spanclass="comment">// cost close to zero.</span></div>
<divclass="line"><aname="l00179"></a><spanclass="lineno"> 179</span> <spanclass="comment">// or if:</span></div>
<divclass="line"><aname="l00180"></a><spanclass="lineno"> 180</span> <spanclass="comment">// - a non-equality constraint (i.e. l <= a.x <= r, with l != r), is at one of</span></div>
<divclass="line"><aname="l00181"></a><spanclass="lineno"> 181</span> <spanclass="comment">// its bounds (a.x = r or a.x = l) and has its dual value close to zero.</span></div>
<divclass="line"><aname="l00184"></a><spanclass="lineno"> 184</span> <spanclass="comment">// Computes derived quantities from the solution.</span></div>
<divclass="line"><aname="l00188"></a><spanclass="lineno"> 188</span> <spanclass="comment">// Computes the primal/dual objectives (without the offset). Note that the</span></div>
<divclass="line"><aname="l00189"></a><spanclass="lineno"> 189</span> <spanclass="comment">// dual objective needs the reduced costs in addition to the dual values.</span></div>
<divclass="line"><aname="l00193"></a><spanclass="lineno"> 193</span> <spanclass="comment">// Given a relative precision on the primal values of up to</span></div>
<divclass="line"><aname="l00194"></a><spanclass="lineno"> 194</span> <spanclass="comment">// solution_feasibility_tolerance(), this returns an upper bound on the</span></div>
<divclass="line"><aname="l00195"></a><spanclass="lineno"> 195</span> <spanclass="comment">// expected precision of the objective.</span></div>
<divclass="line"><aname="l00198"></a><spanclass="lineno"> 198</span> <spanclass="comment">// Returns the max absolute cost pertubation (resp. rhs perturbation) so that</span></div>
<divclass="line"><aname="l00199"></a><spanclass="lineno"> 199</span> <spanclass="comment">// the pair (primal values, dual values) is an EXACT optimal solution to the</span></div>
<divclass="line"><aname="l00200"></a><spanclass="lineno"> 200</span> <spanclass="comment">// perturbed problem. Note that this assumes that</span></div>
<divclass="line"><aname="l00201"></a><spanclass="lineno"> 201</span> <spanclass="comment">// MovePrimalValuesWithinBounds() and MoveDualValuesWithinBounds() have</span></div>
<divclass="line"><aname="l00202"></a><spanclass="lineno"> 202</span> <spanclass="comment">// already been called. The Boolean is_too_large is set to true if any of the</span></div>
<divclass="line"><aname="l00203"></a><spanclass="lineno"> 203</span> <spanclass="comment">// perturbation exceed the tolerance (which depends of the coordinate).</span></div>
<divclass="line"><aname="l00205"></a><spanclass="lineno"> 205</span> <spanclass="comment">// These bounds are computed using the variable and constraint statuses by</span></div>
<divclass="line"><aname="l00206"></a><spanclass="lineno"> 206</span> <spanclass="comment">// enforcing the complementary slackness optimal conditions. Note that they</span></div>
<divclass="line"><aname="l00207"></a><spanclass="lineno"> 207</span> <spanclass="comment">// are almost the same as ComputeActivityInfeasibility() and</span></div>
<divclass="line"><aname="l00208"></a><spanclass="lineno"> 208</span> <spanclass="comment">// ComputeReducedCostInfeasibility() but looks for optimality rather than just</span></div>
<divclass="line"><aname="l00211"></a><spanclass="lineno"> 211</span> <spanclass="comment">// Note(user): We could get EXACT bounds on these perturbations by changing</span></div>
<divclass="line"><aname="l00212"></a><spanclass="lineno"> 212</span> <spanclass="comment">// the rounding mode appropriately during these computations. But this is</span></div>
<divclass="line"><aname="l00213"></a><spanclass="lineno"> 213</span> <spanclass="comment">// probably not needed.</span></div>
<divclass="line"><aname="l00219"></a><spanclass="lineno"> 219</span> <spanclass="comment">// Computes the maximum of the infeasibilities associated with each values.</span></div>
<divclass="line"><aname="l00220"></a><spanclass="lineno"> 220</span> <spanclass="comment">// The returned infeasibilities are the maximum of the "absolute" errors of</span></div>
<divclass="line"><aname="l00221"></a><spanclass="lineno"> 221</span> <spanclass="comment">// each vector coefficients.</span></div>
<divclass="line"><aname="l00223"></a><spanclass="lineno"> 223</span> <spanclass="comment">// These function also set is_too_large to true if any infeasibility is</span></div>
<divclass="line"><aname="l00224"></a><spanclass="lineno"> 224</span> <spanclass="comment">// greater than the tolerance (which depends of the coordinate).</span></div>
<divclass="line"><aname="l00234"></a><spanclass="lineno"> 234</span> <spanclass="comment">// On a call to Solve(), this is initialized to an exact copy of the given</span></div>
<divclass="line"><aname="l00235"></a><spanclass="lineno"> 235</span> <spanclass="comment">// linear program. It is later modified by the preprocessors and then solved</span></div>
<divclass="line"><aname="l00236"></a><spanclass="lineno"> 236</span> <spanclass="comment">// by the revised simplex.</span></div>
<divclass="line"><aname="l00238"></a><spanclass="lineno"> 238</span> <spanclass="comment">// This is not efficient memory-wise but allows to check optimality with</span></div>
<divclass="line"><aname="l00239"></a><spanclass="lineno"> 239</span> <spanclass="comment">// respect to the given LinearProgram that is guaranteed to not have been</span></div>
<divclass="line"><aname="l00240"></a><spanclass="lineno"> 240</span> <spanclass="comment">// modified. It also allows for a nicer Solve() API with a const</span></div>
<divclass="line"><aname="l00247"></a><spanclass="lineno"> 247</span> <spanclass="comment">// The number of revised simplex iterations used by the last Solve().</span></div>
<divclass="line"><aname="l00250"></a><spanclass="lineno"> 250</span> <spanclass="comment">// The current ProblemSolution.</span></div>
<divclass="line"><aname="l00251"></a><spanclass="lineno"> 251</span> <spanclass="comment">// TODO(user): use a ProblemSolution directly?</span></div>
<divclass="line"><aname="l00257"></a><spanclass="lineno"> 257</span> <spanclass="comment">// Quantities computed from the solution and the linear program.</span></div>
<divclass="line"><aname="l00265"></a><spanclass="lineno"> 265</span> <spanclass="comment">// Proto holding all the parameters of the algorithm.</span></div>
<divclass="line"><aname="l00268"></a><spanclass="lineno"> 268</span> <spanclass="comment">// The number of times Solve() was called. Used to number dump files.</span></div>
<divclass="ttc"id="aclassoperations__research_1_1_time_limit_html"><divclass="ttname"><ahref="classoperations__research_1_1_time_limit.html">operations_research::TimeLimit</a></div><divclass="ttdoc">A simple class to enforce both an elapsed time limit and a deterministic time limit in the same threa...</div><divclass="ttdef"><b>Definition:</b><ahref="time__limit_8h_source.html#l00105">time_limit.h:105</a></div></div>
<divclass="ttc"id="aclassoperations__research_1_1glop_1_1_l_p_solver_html_a01f64f8af66c6c5a66d3b4ebc868cab6"><divclass="ttname"><ahref="classoperations__research_1_1glop_1_1_l_p_solver.html#a01f64f8af66c6c5a66d3b4ebc868cab6">operations_research::glop::LPSolver::GetParameters</a></div><divclass="ttdeci">const GlopParameters & GetParameters() const</div><divclass="ttdef"><b>Definition:</b><ahref="lp__solver_8cc_source.html#l00128">lp_solver.cc:128</a></div></div>
<divclass="ttc"id="aclassoperations__research_1_1glop_1_1_l_p_solver_html_a1773941507c0c076dadf389945a07225"><divclass="ttname"><ahref="classoperations__research_1_1glop_1_1_l_p_solver.html#a1773941507c0c076dadf389945a07225">operations_research::glop::LPSolver::constraint_activities</a></div><divclass="ttdeci">const DenseColumn & constraint_activities() const</div><divclass="ttdef"><b>Definition:</b><ahref="lp__solver_8h_source.html#l00113">lp_solver.h:113</a></div></div>
<divclass="ttc"id="aclassoperations__research_1_1glop_1_1_l_p_solver_html_a2fcdc6c1d7ad743bc685f8181ef82a5d"><divclass="ttname"><ahref="classoperations__research_1_1glop_1_1_l_p_solver.html#a2fcdc6c1d7ad743bc685f8181ef82a5d">operations_research::glop::LPSolver::constraint_statuses</a></div><divclass="ttdeci">const ConstraintStatusColumn & constraint_statuses() const</div><divclass="ttdef"><b>Definition:</b><ahref="lp__solver_8h_source.html#l00116">lp_solver.h:116</a></div></div>
<divclass="ttc"id="aclassoperations__research_1_1glop_1_1_l_p_solver_html_a69f41bae06f08e5e85e793c973997ae4"><divclass="ttname"><ahref="classoperations__research_1_1glop_1_1_l_p_solver.html#a69f41bae06f08e5e85e793c973997ae4">operations_research::glop::LPSolver::variable_statuses</a></div><divclass="ttdeci">const VariableStatusRow & variable_statuses() const</div><divclass="ttdef"><b>Definition:</b><ahref="lp__solver_8h_source.html#l00102">lp_solver.h:102</a></div></div>
<divclass="ttc"id="aclassoperations__research_1_1glop_1_1_l_p_solver_html_a6f03b0d76c7cb626253588002dcc500a"><divclass="ttname"><ahref="classoperations__research_1_1glop_1_1_l_p_solver.html#a6f03b0d76c7cb626253588002dcc500a">operations_research::glop::LPSolver::dual_values</a></div><divclass="ttdeci">const DenseColumn & dual_values() const</div><divclass="ttdef"><b>Definition:</b><ahref="lp__solver_8h_source.html#l00112">lp_solver.h:112</a></div></div>
<divclass="ttc"id="aclassoperations__research_1_1glop_1_1_l_p_solver_html_a79f4b1dff56ea4e839e0d380019c4869"><divclass="ttname"><ahref="classoperations__research_1_1glop_1_1_l_p_solver.html#a79f4b1dff56ea4e839e0d380019c4869">operations_research::glop::LPSolver::variable_values</a></div><divclass="ttdeci">const DenseRow & variable_values() const</div><divclass="ttdef"><b>Definition:</b><ahref="lp__solver_8h_source.html#l00100">lp_solver.h:100</a></div></div>
<divclass="ttc"id="aclassoperations__research_1_1glop_1_1_l_p_solver_html_acb55a272bf1c6a463801a3167f2fbdb1"><divclass="ttname"><ahref="classoperations__research_1_1glop_1_1_l_p_solver.html#acb55a272bf1c6a463801a3167f2fbdb1">operations_research::glop::LPSolver::reduced_costs</a></div><divclass="ttdeci">const DenseRow & reduced_costs() const</div><divclass="ttdef"><b>Definition:</b><ahref="lp__solver_8h_source.html#l00101">lp_solver.h:101</a></div></div>
<divclass="ttc"id="anamespaceoperations__research_html"><divclass="ttname"><ahref="namespaceoperations__research.html">operations_research</a></div><divclass="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><divclass="ttdef"><b>Definition:</b><ahref="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
