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<div class="headertitle"><div class="title">rays.cc</div></div>
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<a href="rays_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include "<a class="code" href="rays_8h.html">ortools/math_opt/solvers/glpk/rays.h</a>"</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <optional></span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <string></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <utility></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</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/status.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/status/statusor.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 "absl/strings/str_cat.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="base_2logging_8h.html">ortools/base/logging.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="base_2status__macros_8h.html">ortools/base/status_macros.h</a>"</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include "<a class="code" href="glpk__computational__form_8h.html">ortools/glpk/glpk_computational_form.h</a>"</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include "<a class="code" href="glpk__formatters_8h.html">ortools/glpk/glpk_formatters.h</a>"</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
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<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_1_1math__opt.html">operations_research::math_opt</a> {</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span>absl::StatusOr<GlpkRay> ComputePrimalRay(glp_prob* <span class="keyword">const</span> problem,</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">const</span> <span class="keywordtype">int</span> non_basic_variable) {</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cstrs = glp_get_num_rows(problem);</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// Check that the non_basic_variable is indeed non basic.</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">const</span> <span class="keywordtype">int</span> non_basic_variable_status =</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <a class="code hl_function" href="namespaceoperations__research.html#a3017e52db1c2688aa77b569b9f7a7b19">ComputeFormVarStatus</a>(problem,</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">/*num_cstrs=*/</span>num_cstrs,</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">/*k=*/</span>non_basic_variable);</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <a class="code hl_define" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(non_basic_variable_status, GLP_BS);</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// When we perform the (primal) simplex algorithm, we detect the primal</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// unboundness when we have a non-basic variable (here variable can be a</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// structural or an auxiliary variable) which contributes to increase (for</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// maximization, decrease for minimization) the objective but none of the</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// basic variables bounds are limiting its growth. GLPK returns the index of</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// this non-basic tableau variable.</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// To be more precise, here we will use the conventions used in</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// glpk-5.0/doc/glpk.pdf available from glpk-5.0.tar.gz.</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// From (glpk eq. 3.13) we know that the values of the basic variables are</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// dependent on the values of the non-basic ones:</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// x_B = 𝚵 x_N</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// where 𝚵 is the tableau defined by (glpk eq. 3.12):</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// 𝚵 = -B^-1 N</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// Thus if the c-th non basic variable is changed:</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// x'_N = x_N + t e_c , e_c ∈ R^n is the c-th standard unit vector</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// t ∈ R is the change</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// Then to keep the primal feasible we must have:</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// x'_B = 𝚵 x'_N</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// = 𝚵 x_N + t 𝚵 e_c</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// = 𝚵 x_N + t 𝚵 e_c</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// = x_B + t 𝚵 e_c</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// We thus have the primal ray:</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// x'_N - x_N = t e_c</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// x'_B - x_B = t 𝚵 e_c</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// From (glpk eq. 3.34) we know that the primal objective is:</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">// z = d^T x_N + c_0</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// I.e. reduced cost d_j shows how the non-basic variable x_j influences the</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// objective.</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// Thus if the problem is a minimization we know that:</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// t > 0 , if d_c < 0</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// t < 0 , if d_c > 0</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// Since if it was not the case, the primal simplex algorithm would not have</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// picked this variable.</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">// The signs for a maximization are reversed:</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// t < 0 , if d_c < 0</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// t > 0 , if d_c > 0</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">const</span> <span class="keywordtype">double</span> reduced_cost = <a class="code hl_function" href="namespaceoperations__research.html#a78b479e166142f91a81aa29b32f3f2bd">ComputeFormVarReducedCost</a>(</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> problem, <span class="comment">/*num_cstrs=*/</span>num_cstrs, <span class="comment">/*k=*/</span>non_basic_variable);</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keyword">const</span> <span class="keywordtype">double</span> t = (glp_get_obj_dir(problem) == GLP_MAX ? 1.0 : -1.0) *</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> (reduced_cost >= 0 ? 1.0 : -1.0);</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
|
|
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// In case of bounded variables, we can check that the result agrees with the</span></div>
|
|
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// current active bound. We can't do so for free variables though.</span></div>
|
|
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">switch</span> (non_basic_variable_status) {</div>
|
|
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordflow">case</span> GLP_NL: <span class="comment">// At lower-bound.</span></div>
|
|
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordflow">if</span> (t == -1.0) {</div>
|
|
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">return</span> absl::InternalError(</div>
|
|
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="stringliteral">"a non-basic variable at its lower-bound is reported as cause of "</span></div>
|
|
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="stringliteral">"unboundness but the reduced cost's sign indicates that the solver "</span></div>
|
|
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="stringliteral">"considered making it smaller"</span>);</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"> 113</span> <span class="keywordflow">break</span>;</div>
|
|
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">case</span> GLP_NU: <span class="comment">// At upper-bound.</span></div>
|
|
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordflow">if</span> (t == 1.0) {</div>
|
|
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordflow">return</span> absl::InternalError(</div>
|
|
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="stringliteral">"a non-basic variable at its upper-bound is reported as cause of "</span></div>
|
|
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="stringliteral">"unboundness but the reduced cost's sign indicates that the solver "</span></div>
|
|
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="stringliteral">"considered making it bigger"</span>);</div>
|
|
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> }</div>
|
|
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordflow">break</span>;</div>
|
|
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">case</span> GLP_NF: <span class="comment">// Free (unbounded).</span></div>
|
|
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">break</span>;</div>
|
|
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">default</span>: <span class="comment">// GLP_BS (basic), GLP_NS (fixed) or invalid value</span></div>
|
|
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">return</span> absl::InternalError(absl::StrCat(</div>
|
|
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="stringliteral">"unexpected "</span>, <a class="code hl_function" href="namespaceoperations__research.html#a190d88f2f236423afb5ff49fe3a31217">BasisStatusString</a>(non_basic_variable_status),</div>
|
|
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="stringliteral">" reported as cause of unboundness"</span>));</div>
|
|
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
|
|
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
|
|
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <a class="code hl_typedef" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd">GlpkRay::SparseVector</a> ray_non_zeros;</div>
|
|
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
|
|
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// As seen in the maths above:</span></div>
|
|
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// x'_N - x_N = t e_c</span></div>
|
|
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> ray_non_zeros.emplace_back(non_basic_variable, t);</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"> 138</span> <span class="comment">// As seen in the maths above:</span></div>
|
|
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="comment">// x'_B - x_B = t 𝚵 e_c</span></div>
|
|
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// Here 𝚵 e_c is the c-th column of the tableau. We thus use the GLPK function</span></div>
|
|
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="comment">// that returns this column.</span></div>
|
|
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> std::vector<int> inds(num_cstrs + 1);</div>
|
|
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> std::vector<double> vals(num_cstrs + 1);</div>
|
|
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keyword">const</span> <span class="keywordtype">int</span> non_zeros =</div>
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|
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> glp_eval_tab_col(problem, non_basic_variable, inds.data(), vals.data());</div>
|
|
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i <= non_zeros; ++i) {</div>
|
|
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> ray_non_zeros.emplace_back(inds[i], t * vals[i]);</div>
|
|
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> }</div>
|
|
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
|
|
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">return</span> GlpkRay(<a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a168c8e12a7f30e09240e40ae392f3c1e">GlpkRayType::kPrimal</a>, std::move(ray_non_zeros));</div>
|
|
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span>}</div>
|
|
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
|
|
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span>absl::StatusOr<GlpkRay> ComputeDualRay(glp_prob* <span class="keyword">const</span> problem,</div>
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|
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">const</span> <span class="keywordtype">int</span> basic_variable) {</div>
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|
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cstrs = glp_get_num_rows(problem);</div>
|
|
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
|
|
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// Check that the basic_variable is indeed basic.</span></div>
|
|
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> {</div>
|
|
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d">status</a> = <a class="code hl_function" href="namespaceoperations__research.html#a3017e52db1c2688aa77b569b9f7a7b19">ComputeFormVarStatus</a>(problem,</div>
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|
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="comment">/*num_cstrs=*/</span>num_cstrs,</div>
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|
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="comment">/*k=*/</span>basic_variable);</div>
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|
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(<a class="code hl_variable" href="g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d">status</a>, GLP_BS) << <a class="code hl_function" href="namespaceoperations__research.html#a190d88f2f236423afb5ff49fe3a31217">BasisStatusString</a>(<a class="code hl_variable" href="g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d">status</a>);</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> }</div>
|
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> </div>
|
|
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// The dual simplex proceeds by repeatedly finding basic variables (here</span></div>
|
|
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// variable includes structural and auxiliary variables) that are primal</span></div>
|
|
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="comment">// infeasible and replacing them in the basis with a non-basic variable whose</span></div>
|
|
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// growth is limited by their reduced cost.</span></div>
|
|
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// This algorithm detects dual unboundness when we have a basic variable is</span></div>
|
|
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// primal infeasible (out of its bounds) but there are no non-basic variable</span></div>
|
|
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// that would limit the growth of its reduced cost, and thus the growth of the</span></div>
|
|
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// dual objective.</span></div>
|
|
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// To be more precise, here we will use the conventions used in</span></div>
|
|
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// glpk-5.0/doc/glpk.pdf available from glpk-5.0.tar.gz. The dual simplex</span></div>
|
|
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// algorithm is defined by (https://d-nb.info/978580478/34): Koberstein,</span></div>
|
|
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// Achim. "The dual simplex method, techniques for a fast and stable</span></div>
|
|
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// implementation." Unpublished doctoral thesis, Universität Paderborn,</span></div>
|
|
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// Paderborn, Germany (2005).</span></div>
|
|
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// In the following reasoning, we will considering the dual after the</span></div>
|
|
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="comment">// permutation of the basis (glpk eq. 3.27):</span></div>
|
|
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="comment">// B^T π + λ_B = c_B</span></div>
|
|
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="comment">// N^T π + λ_N = c_N</span></div>
|
|
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// We will now see what happens when we relax a basic variable that would</span></div>
|
|
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// leave the base. See (Koberstein §3.1.2) for details.</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">// Let's assume we have (π, λ_B, λ_N) that is a basic dual feasible</span></div>
|
|
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="comment">// solution. By definition:</span></div>
|
|
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="comment">// λ_B = 0</span></div>
|
|
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// If we relax the equality constraint of the basic variable r that is primal</span></div>
|
|
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// infeasible, that is if we relax λ_B_r and get another solution (π', λ'_B,</span></div>
|
|
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// λ'_N). By definition, all other basic variables stays at equality and thus:</span></div>
|
|
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="comment">// λ'_B = t e_r , e_r ∈ R^m is the standard unit vector</span></div>
|
|
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="comment">// t ∈ R is the relaxation</span></div>
|
|
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="comment">// From (glpk eq. 3.30) we have:</span></div>
|
|
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// λ'_N = N^T B^-T λ'_B + (c_N - N^T B^-T c_B)</span></div>
|
|
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// λ'_N = t (B^-1 N)^T e_r + λ_N</span></div>
|
|
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="comment">// Using the (glpk eq. 3.12) definition of the tableau:</span></div>
|
|
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="comment">// 𝚵 = -B^-1 N</span></div>
|
|
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="comment">// We have:</span></div>
|
|
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// λ'_N = -t 𝚵^T e_r + λ_N</span></div>
|
|
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="comment">// That is that the change of the reduced cost of the basic variable r has to</span></div>
|
|
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="comment">// be compensated by the change of the reduced costs the non-basic variables.</span></div>
|
|
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="comment">// We can write the new dual objective:</span></div>
|
|
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="comment">// Z' = l^T λ'_l + u^T λ'_u</span></div>
|
|
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="comment">// If the problem is a minimization we have:</span></div>
|
|
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="comment">// Z' = sum_{j:λ'_N_j >= 0} l_N_j λ'_N_j +</span></div>
|
|
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="comment">// sum_{j:λ'_N_j <= 0} u_N_j λ'_N_j +</span></div>
|
|
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="comment">// {l_B_r, if t >= 0, u_B_r, else} t</span></div>
|
|
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="comment">// Here we assume the signs of λ'_N are identical to the ones of λ_N (this is</span></div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="comment">// not an issue with dual simplex since we want to make one non-basic tight to</span></div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="comment">// use it in the basis) we can replace λ'_N with the value computed above and</span></div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="comment">// considering the initial solution was basic which implied that non-basic</span></div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="comment">// where at their bound we can rewrite the objective as:</span></div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="comment">// Z' = Z - t e_r^T 𝚵 x_N + {l_B_r, if t >= 0, u_B_r, else} t</span></div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="comment">// We have, using (glpk eq. 3.13):</span></div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="comment">// e_r^T 𝚵 x_N = e_r^T x_B = x_B_r</span></div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="comment">// And thus, for a minimization we have:</span></div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="comment">// Z' - Z = t * {l_B_r - x_B_r, if t >= 0,</span></div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// u_B_r - x_B_r, if t <= 0}</span></div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="comment">// Depending on the type of constraint, i.e. depending on whether l_B_r and/or</span></div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="comment">// u_B_r are finite), we have constraints on the sign of `t`. But we can see</span></div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// that since we pick the basic variable r because it was primal infeasible,</span></div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="comment">// then it should break one of its finite bounds.</span></div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="comment">// either x_B_r < l_B_r</span></div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="comment">// or u_B_r < x_B_r</span></div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="comment">// If l_B_r is finite and x_B_r < l_B_r, then choosing:</span></div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="comment">// t >= 0</span></div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="comment">// leads to:</span></div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="comment">// Z' - Z >= 0</span></div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="comment">// and we see from (glpk eq. 3.17) and the "rule of signs" table (glpk page</span></div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> <span class="comment">// 101) that we keep the solution dual feasible by doing so.</span></div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="comment">// The same logic applies if x_B_r > u_B_r:</span></div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <span class="comment">// t <= 0</span></div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <span class="comment">// leads to:</span></div>
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|
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="comment">// Z' - Z >= 0</span></div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="comment">// The dual objective increase in both cases; which is what we want for a</span></div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="comment">// minimization problem since the dual is a maximization.</span></div>
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|
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> <span class="comment">// For a maximization problem the results are similar but the sign of t</span></div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="comment">// changes (which is expected since the dual is a minimization):</span></div>
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|
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="comment">// Z' - Z = t * {l_B_r - x_B_r, if t <= 0,</span></div>
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|
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="comment">// u_B_r - x_B_r, if t >= 0}</span></div>
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|
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="comment">// If a problem is dual unbounded, this means that it is possible to grow t</span></div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="comment">// without limit. I.e. is possible to choose any value for t without making</span></div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="comment">// any λ'_N change sign.</span></div>
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|
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="comment">// We can then express the changes of λ' from t:</span></div>
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|
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="comment">// λ'_B = t e_r</span></div>
|
|
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="comment">// λ'_N = -t 𝚵^T e_r + λ_N</span></div>
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|
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <span class="comment">// Since λ_B = 0, we can rewrite those as:</span></div>
|
|
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="comment">// λ'_B - λ_B = t e_r</span></div>
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|
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="comment">// λ'_N - λ_N = -t 𝚵^T e_r</span></div>
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|
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <span class="comment">// That is the dual ray.</span></div>
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|
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_value = <a class="code hl_function" href="namespaceoperations__research.html#a08778ed3d6825737a554d34700015bde">ComputeFormVarPrimalValue</a>(</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> problem, <span class="comment">/*num_cstrs=*/</span>num_cstrs, <span class="comment">/*k=*/</span>basic_variable);</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> </div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a> = <a class="code hl_function" href="namespaceoperations__research.html#ae8092de2472a0ac3308c39609792e6fb">ComputeFormVarUpperBound</a>(</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> problem, <span class="comment">/*num_cstrs=*/</span>num_cstrs, <span class="comment">/*k=*/</span>basic_variable);</div>
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|
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a> = <a class="code hl_function" href="namespaceoperations__research.html#ab1175b5bb75d496f60b63e49399e1818">ComputeFormVarLowerBound</a>(</div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> problem, <span class="comment">/*num_cstrs=*/</span>num_cstrs, <span class="comment">/*k=*/</span>basic_variable);</div>
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|
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keywordflow">if</span> (!(primal_value > <a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a> || primal_value < <a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>)) {</div>
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|
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="keywordflow">return</span> absl::InternalError(</div>
|
|
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <span class="stringliteral">"dual ray computation failed: GLPK identified a basic variable as the "</span></div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> <span class="stringliteral">"source of unboundness but its primal value is within its bounds"</span>);</div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> }</div>
|
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> </div>
|
|
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <span class="comment">// As we have seen in the maths above, depending on which primal bound is</span></div>
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|
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> <span class="comment">// violated and the optimization direction, we choose the sign of t.</span></div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> <span class="comment">// Here the problem is unbounded so we can pick any value for t we want.</span></div>
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|
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> <span class="keyword">const</span> <span class="keywordtype">double</span> t = (glp_get_obj_dir(problem) == GLP_MAX ? 1.0 : -1.0) *</div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> (primal_value > <a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a> ? 1.0 : -1.0);</div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> </div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> <a class="code hl_typedef" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd">GlpkRay::SparseVector</a> ray_non_zeros;</div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> </div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> <span class="comment">// As seen in the math above:</span></div>
|
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> <span class="comment">// λ'_B - λ_B = t e_r</span></div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> ray_non_zeros.emplace_back(basic_variable, t);</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> </div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> <span class="comment">// As we have seen above, to keep the dual feasible, we must update the</span></div>
|
|
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> <span class="comment">// reduced costs of the non-basic variables by the formula:</span></div>
|
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> <span class="comment">// λ'_N - λ_N = -t 𝚵^T e_r</span></div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="comment">// Here 𝚵^T e_r is the r-th row of the tableau. We thus use the GLPK function</span></div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> <span class="comment">// that returns this row.</span></div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_structural_vars = glp_get_num_cols(problem);</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> std::vector<int> inds(num_structural_vars + 1);</div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> std::vector<double> vals(num_structural_vars + 1);</div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <span class="keyword">const</span> <span class="keywordtype">int</span> non_zeros =</div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> glp_eval_tab_row(problem, basic_variable, inds.data(), vals.data());</div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i <= non_zeros; ++i) {</div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> ray_non_zeros.emplace_back(inds[i], -t * vals[i]);</div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> }</div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> </div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <span class="keywordflow">return</span> GlpkRay(<a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a853ead83f7e75b38bba794318254dc91">GlpkRayType::kDual</a>, std::move(ray_non_zeros));</div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span>}</div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> </div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span>} <span class="comment">// namespace</span></div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> </div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a488c6f810ff77a3759d6900693105bdd"> 348</a></span><a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a488c6f810ff77a3759d6900693105bdd">GlpkRay::GlpkRay</a>(<span class="keyword">const</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7">GlpkRayType</a> type, <a class="code hl_typedef" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd">SparseVector</a> non_zero_components)</div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> : type(type), non_zero_components(<a class="code hl_namespace" href="namespacestd.html">std</a>::move(non_zero_components)) {}</div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> </div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1math__opt.html#aa3bcd3f312f5746e50d53bd5a8dedd2a"> 351</a></span>absl::StatusOr<std::optional<GlpkRay>> <a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#aa3bcd3f312f5746e50d53bd5a8dedd2a">GlpkComputeUnboundRay</a>(</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> glp_prob* <span class="keyword">const</span> problem) {</div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <span class="keyword">const</span> <span class="keywordtype">int</span> unbound_ray = glp_get_unbnd_ray(problem);</div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> <span class="keywordflow">if</span> (unbound_ray <= 0) {</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="comment">// No ray, do nothing.</span></div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(unbound_ray, 0);</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> <span class="keywordflow">return</span> std::nullopt;</div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> }</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> </div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> <span class="comment">// The factorization may not exists when GLPK's trivial_lp() is used to solve</span></div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="comment">// a trivial LP. Here we force the computation of the factorization if</span></div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <span class="comment">// necessary.</span></div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> <span class="keywordflow">if</span> (!glp_bf_exists(problem)) {</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> <span class="keyword">const</span> <span class="keywordtype">int</span> factorization_rc = glp_factorize(problem);</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> <span class="keywordflow">if</span> (factorization_rc != 0) {</div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>() << <span class="stringliteral">"glp_factorize() failed: "</span></div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> << <a class="code hl_function" href="namespaceoperations__research.html#a90d45f14d9a74cb49094695918d444d8">ReturnCodeString</a>(factorization_rc);</div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> }</div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> }</div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> </div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="comment">// The function glp_get_unbnd_ray() returns either:</span></div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="comment">// - a non-basic tableau variable if we have primal unboundness.</span></div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> <span class="comment">// - a basic tableau variable if we have dual unboundness.</span></div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> is_dual_ray =</div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <a class="code hl_function" href="namespaceoperations__research.html#a3017e52db1c2688aa77b569b9f7a7b19">ComputeFormVarStatus</a>(problem,</div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="comment">/*num_cstrs=*/</span>glp_get_num_rows(problem),</div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> <span class="comment">/*k=*/</span>unbound_ray) == GLP_BS;</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html">GlpkRay</a> ray,</div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> (is_dual_ray ? ComputeDualRay(problem, unbound_ray)</div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> : ComputePrimalRay(problem, unbound_ray)));</div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> <span class="keywordflow">return</span> ray;</div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span>}</div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> </div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span>} <span class="comment">// namespace operations_research::math_opt</span></div>
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a7c0ce053b28d53aa4eaf3eb7fb71663b"><div class="ttname"><a href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a></div><div class="ttdeci">#define CHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00703">base/logging.h:703</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ab25e01a2942b821d66371fc68d53f2eb"><div class="ttname"><a href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a></div><div class="ttdeci">#define CHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00704">base/logging.h:704</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0"><div class="ttname"><a href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a></div><div class="ttdeci">#define DCHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00891">base/logging.h:891</a></div></div>
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<div class="ttc" id="abase_2status__macros_8h_html"><div class="ttname"><a href="base_2status__macros_8h.html">status_macros.h</a></div></div>
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<div class="ttc" id="abase_2status__macros_8h_html_a600de4b8f65fe0a4b1898041634f9011"><div class="ttname"><a href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a></div><div class="ttdeci">#define ASSIGN_OR_RETURN(lhs, rexpr)</div><div class="ttdef"><b>Definition:</b> <a href="base_2status__macros_8h_source.html#l00046">base/status_macros.h:46</a></div></div>
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<div class="ttc" id="ag__gurobi_8cc_html_a2237393c7ae7ad7344c9885066d5ab6d"><div class="ttname"><a href="g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d">status</a></div><div class="ttdeci">absl::Status status</div><div class="ttdef"><b>Definition:</b> <a href="g__gurobi_8cc_source.html#l00035">g_gurobi.cc:35</a></div></div>
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<div class="ttc" id="aglpk__computational__form_8h_html"><div class="ttname"><a href="glpk__computational__form_8h.html">glpk_computational_form.h</a></div></div>
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<div class="ttc" id="aglpk__formatters_8h_html"><div class="ttname"><a href="glpk__formatters_8h.html">glpk_formatters.h</a></div></div>
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<div class="ttc" id="agscip__solver_8cc_html_a1ba5ca0f61f2fa13bd23bf0f89004f35"><div class="ttname"><a href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a></div><div class="ttdeci">double upper_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00137">gscip_solver.cc:137</a></div></div>
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<div class="ttc" id="agscip__solver_8cc_html_a1e2f9a2352c1d9a6cada9544898fceec"><div class="ttname"><a href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a></div><div class="ttdeci">double lower_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00136">gscip_solver.cc:136</a></div></div>
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<div class="ttc" id="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>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_aa3bcd3f312f5746e50d53bd5a8dedd2a"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#aa3bcd3f312f5746e50d53bd5a8dedd2a">operations_research::math_opt::GlpkComputeUnboundRay</a></div><div class="ttdeci">absl::StatusOr< std::optional< GlpkRay > > GlpkComputeUnboundRay(glp_prob *const problem)</div><div class="ttdef"><b>Definition:</b> <a href="rays_8cc_source.html#l00351">rays.cc:351</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_ad6ffe3747921431333fa443d04f0dcd7"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7">operations_research::math_opt::GlpkRayType</a></div><div class="ttdeci">GlpkRayType</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00033">rays.h:33</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_ad6ffe3747921431333fa443d04f0dcd7a168c8e12a7f30e09240e40ae392f3c1e"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a168c8e12a7f30e09240e40ae392f3c1e">operations_research::math_opt::kPrimal</a></div><div class="ttdeci">@ kPrimal</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00039">rays.h:39</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_ad6ffe3747921431333fa443d04f0dcd7a853ead83f7e75b38bba794318254dc91"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a853ead83f7e75b38bba794318254dc91">operations_research::math_opt::kDual</a></div><div class="ttdeci">@ kDual</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00046">rays.h:46</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a08778ed3d6825737a554d34700015bde"><div class="ttname"><a href="namespaceoperations__research.html#a08778ed3d6825737a554d34700015bde">operations_research::ComputeFormVarPrimalValue</a></div><div class="ttdeci">double ComputeFormVarPrimalValue(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00108">glpk_computational_form.h:108</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a190d88f2f236423afb5ff49fe3a31217"><div class="ttname"><a href="namespaceoperations__research.html#a190d88f2f236423afb5ff49fe3a31217">operations_research::BasisStatusString</a></div><div class="ttdeci">std::string BasisStatusString(const int stat)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__formatters_8cc_source.html#l00048">glpk_formatters.cc:48</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a3017e52db1c2688aa77b569b9f7a7b19"><div class="ttname"><a href="namespaceoperations__research.html#a3017e52db1c2688aa77b569b9f7a7b19">operations_research::ComputeFormVarStatus</a></div><div class="ttdeci">int ComputeFormVarStatus(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00088">glpk_computational_form.h:88</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a78b479e166142f91a81aa29b32f3f2bd"><div class="ttname"><a href="namespaceoperations__research.html#a78b479e166142f91a81aa29b32f3f2bd">operations_research::ComputeFormVarReducedCost</a></div><div class="ttdeci">double ComputeFormVarReducedCost(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00098">glpk_computational_form.h:98</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a90d45f14d9a74cb49094695918d444d8"><div class="ttname"><a href="namespaceoperations__research.html#a90d45f14d9a74cb49094695918d444d8">operations_research::ReturnCodeString</a></div><div class="ttdeci">std::string ReturnCodeString(const int rc)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__formatters_8cc_source.html#l00065">glpk_formatters.cc:65</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ab1175b5bb75d496f60b63e49399e1818"><div class="ttname"><a href="namespaceoperations__research.html#ab1175b5bb75d496f60b63e49399e1818">operations_research::ComputeFormVarLowerBound</a></div><div class="ttdeci">double ComputeFormVarLowerBound(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00118">glpk_computational_form.h:118</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ae8092de2472a0ac3308c39609792e6fb"><div class="ttname"><a href="namespaceoperations__research.html#ae8092de2472a0ac3308c39609792e6fb">operations_research::ComputeFormVarUpperBound</a></div><div class="ttdeci">double ComputeFormVarUpperBound(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00128">glpk_computational_form.h:128</a></div></div>
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<div class="ttc" id="anamespacestd_html"><div class="ttname"><a href="namespacestd.html">std</a></div><div class="ttdoc">STL namespace.</div></div>
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<div class="ttc" id="anamespaceutil_html_a302ee4bfcb86ea9ed64a193ed0b14648"><div class="ttname"><a href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a></div><div class="ttdeci">StatusBuilder InternalErrorBuilder()</div><div class="ttdef"><b>Definition:</b> <a href="status__builder_8h_source.html#l00084">status_builder.h:84</a></div></div>
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<div class="ttc" id="arays_8h_html"><div class="ttname"><a href="rays_8h.html">rays.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_glpk_ray_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_glpk_ray.html">operations_research::math_opt::GlpkRay</a></div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00055">rays.h:55</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_glpk_ray_html_a488c6f810ff77a3759d6900693105bdd"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a488c6f810ff77a3759d6900693105bdd">operations_research::math_opt::GlpkRay::GlpkRay</a></div><div class="ttdeci">GlpkRay(GlpkRayType type, SparseVector non_zero_components)</div><div class="ttdef"><b>Definition:</b> <a href="rays_8cc_source.html#l00348">rays.cc:348</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_glpk_ray_html_ab6e7a7fab6fd3cfc7263644c7ede57bd"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd">operations_research::math_opt::GlpkRay::SparseVector</a></div><div class="ttdeci">std::vector< std::pair< int, double > > SparseVector</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00056">rays.h:56</a></div></div>
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