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<a href="entering__variable_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include "<a class="code" href="entering__variable_8h.html">ortools/glop/entering_variable.h</a>"</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <queue></span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include "<a class="code" href="timer_8h.html">ortools/base/timer.h</a>"</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "<a class="code" href="lp__data_2lp__utils_8h.html">ortools/lp_data/lp_utils.h</a>"</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "<a class="code" href="port_2proto__utils_8h.html">ortools/port/proto_utils.h</a>"</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">namespace </span>glop {</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div><div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_entering_variable.html#a2dbed549d25654617b466ea86d51fa51"> 25</a></span> <a class="code" href="classoperations__research_1_1glop_1_1_entering_variable.html#a2dbed549d25654617b466ea86d51fa51">EnteringVariable::EnteringVariable</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_variables_info.html">VariablesInfo</a>& variables_info,</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  absl::BitGenRef random,</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <a class="code" href="classoperations__research_1_1glop_1_1_reduced_costs.html">ReducedCosts</a>* reduced_costs)</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  : variables_info_(variables_info),</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  random_(random),</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  reduced_costs_(reduced_costs),</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  parameters_() {}</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> </div><div class="line"><a name="l00033"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_entering_variable.html#afaf135d40c257d0f1a49aa8e795c9b03"> 33</a></span> <a class="code" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code" href="classoperations__research_1_1glop_1_1_entering_variable.html#afaf135d40c257d0f1a49aa8e795c9b03">EnteringVariable::DualChooseEnteringColumn</a>(</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordtype">bool</span> nothing_to_recompute, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_update_row.html">UpdateRow</a>& update_row,</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> cost_variation, std::vector<ColIndex>* bound_flip_candidates,</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  ColIndex* entering_col) {</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <a class="code" href="status_8h.html#ae9a90d3e61ffae636234f2c1283117d8">GLOP_RETURN_ERROR_IF_NULL</a>(entering_col);</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& update_coefficient = update_row.<a class="code" href="classoperations__research_1_1glop_1_1_update_row.html#a30fddb9e35865ba28420bd52538a183f">GetCoefficients</a>();</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& reduced_costs = reduced_costs_-><a class="code" href="classoperations__research_1_1glop_1_1_reduced_costs.html#a9f7d17ed171863f104fbb2a450f89251">GetReducedCosts</a>();</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <a class="code" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> </div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  breakpoints_.clear();</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  breakpoints_.reserve(update_row.<a class="code" href="classoperations__research_1_1glop_1_1_update_row.html#af8e957f1c8389089554ded7bd2b7b45f">GetNonZeroPositions</a>().size());</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_bitset64.html">DenseBitRow</a>& can_decrease = variables_info_.<a class="code" href="classoperations__research_1_1glop_1_1_variables_info.html#a71d4734d51e7037c043b68a74bd7857f">GetCanDecreaseBitRow</a>();</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_bitset64.html">DenseBitRow</a>& can_increase = variables_info_.<a class="code" href="classoperations__research_1_1glop_1_1_variables_info.html#a6cc56ab5da3a82aa2793d18a37f422c4">GetCanIncreaseBitRow</a>();</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_bitset64.html">DenseBitRow</a>& is_boxed = variables_info_.<a class="code" href="classoperations__research_1_1glop_1_1_variables_info.html#a505af340486fcf70ee83abb32e31a628">GetNonBasicBoxedVariables</a>();</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="comment">// If everything has the best possible precision currently, we ignore</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// low coefficients. This make sure we will never choose a pivot too small. It</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">// however can degrade the dual feasibility of the solution, but we can always</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="comment">// fix that later.</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">//</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">// TODO(user): It is unclear if this is a good idea, but the primal simplex</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="comment">// have pretty good/stable behavior with a similar logic. Experiment seems</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="comment">// to show that this works well with the dual too.</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> threshold = nothing_to_recompute</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  ? parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#a68285ca7ffce0d4295c9ce20414eaec4">minimum_acceptable_pivot</a>()</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  : parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#a802ffefaec0732058182bb426e8edbd2">ratio_test_zero_threshold</a>();</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">// Harris ratio test. See below for more explanation. Here this is used to</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// prune the first pass by not enqueueing ColWithRatio for columns that have</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// a ratio greater than the current harris_ratio.</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> harris_tolerance =</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#a40a2f57f5c801d77d6af1848383a4171">harris_tolerance_ratio</a>() *</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  reduced_costs_-><a class="code" href="classoperations__research_1_1glop_1_1_reduced_costs.html#aa6a9551b792028d16dc7123c80f429d1">GetDualFeasibilityTolerance</a>();</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> harris_ratio = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<Fractional>::max</a>();</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// Like for the primal, we always allow a positive ministep, even if a</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// variable is already infeasible by more than the tolerance.</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> minimum_delta =</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#aad2c4edf11b93e46bae7f18ebd43301c">degenerate_ministep_factor</a>() *</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  reduced_costs_-><a class="code" href="classoperations__research_1_1glop_1_1_reduced_costs.html#aa6a9551b792028d16dc7123c80f429d1">GetDualFeasibilityTolerance</a>();</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> </div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  num_operations_ += 10 * update_row.<a class="code" href="classoperations__research_1_1glop_1_1_update_row.html#af8e957f1c8389089554ded7bd2b7b45f">GetNonZeroPositions</a>().size();</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : update_row.<a class="code" href="classoperations__research_1_1glop_1_1_update_row.html#af8e957f1c8389089554ded7bd2b7b45f">GetNonZeroPositions</a>()) {</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">// We will add ratio * coeff to this column with a ratio positive or zero.</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">// cost_variation makes sure the leaving variable will be dual-feasible</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="comment">// (its update coeff is sign(cost_variation) * 1.0).</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> coeff = (cost_variation > 0.0) ? update_coefficient[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  : -update_coefficient[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// In this case, at some point the reduced cost will be positive if not</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// already, and the column will be dual-infeasible.</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordflow">if</span> (can_decrease.<a class="code" href="classoperations__research_1_1_bitset64.html#aa454a4099ee887726b8f5b4a8ed1a81d">IsSet</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) && coeff > threshold) {</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">if</span> (!is_boxed[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) {</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">if</span> (-reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] > harris_ratio * coeff) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  harris_ratio = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  harris_ratio, (-reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] + harris_tolerance) / coeff);</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  harris_ratio = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(minimum_delta / coeff, harris_ratio);</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  }</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  breakpoints_.push_back(ColWithRatio(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, -reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>], coeff));</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  }</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="comment">// In this case, at some point the reduced cost will be negative if not</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// already, and the column will be dual-infeasible.</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">if</span> (can_increase.<a class="code" href="classoperations__research_1_1_bitset64.html#aa454a4099ee887726b8f5b4a8ed1a81d">IsSet</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) && coeff < -threshold) {</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">if</span> (!is_boxed[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) {</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">if</span> (reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] > harris_ratio * -coeff) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  harris_ratio = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  harris_ratio, (reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] + harris_tolerance) / -coeff);</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  harris_ratio = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(minimum_delta / -coeff, harris_ratio);</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  }</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  breakpoints_.push_back(ColWithRatio(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>], -coeff));</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  }</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  }</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span> </div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="comment">// Process the breakpoints in priority order as suggested by Maros in</span></div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">// I. Maros, "A generalized dual phase-2 simplex algorithm", European Journal</span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="comment">// of Operational Research, 149(1):1-16, 2003.</span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="comment">// We use directly make_heap() to avoid a copy of breakpoints, benchmark shows</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="comment">// that it is slightly faster.</span></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  std::make_heap(breakpoints_.begin(), breakpoints_.end());</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">// Harris ratio test. Since we process the breakpoints by increasing ratio, we</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// do not need a two-pass algorithm as described in the literature. Each time</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// we process a new breakpoint, we update the harris_ratio of all the</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// processed breakpoints. For the first new breakpoint with a ratio greater</span></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// than the current harris_ratio we know that:</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// - All the unprocessed breakpoints will have a ratio greater too, so they</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">// will not contribute to the minimum Harris ratio.</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// - We thus have the actual harris_ratio.</span></div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">// - We have processed all breakpoints with a ratio smaller than it.</span></div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  harris_ratio = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<Fractional>::max</a>();</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> </div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  *entering_col = <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>;</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  bound_flip_candidates->clear();</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> step = 0.0;</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> best_coeff = -1.0;</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> variation_magnitude = std::abs(cost_variation);</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  equivalent_entering_choices_.clear();</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordflow">while</span> (!breakpoints_.empty()) {</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keyword">const</span> ColWithRatio top = breakpoints_.front();</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">if</span> (top.ratio > harris_ratio) <span class="keywordflow">break</span>;</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="comment">// If the column is boxed, we can just switch its bounds and</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="comment">// ignore the breakpoint! But we need to see if the entering row still</span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">// improve the objective. This is called the bound flipping ratio test in</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="comment">// the literature. See for instance:</span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="comment">// http://www.mpi-inf.mpg.de/conferences/adfocs-03/Slides/Bixby_2.pdf</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="comment">//</span></div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// For each bound flip, |cost_variation| decreases by</span></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="comment">// |upper_bound - lower_bound| times |coeff|.</span></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="comment">//</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="comment">// Note that the actual flipping will be done afterwards by</span></div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// MakeBoxedVariableDualFeasible() in revised_simplex.cc.</span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">if</span> (variation_magnitude > threshold) {</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">if</span> (is_boxed[top.col]) {</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  variation_magnitude -=</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  variables_info_.<a class="code" href="classoperations__research_1_1glop_1_1_variables_info.html#a611fb1da73c33e2716b380db980fa825">GetBoundDifference</a>(top.col) * top.coeff_magnitude;</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">if</span> (variation_magnitude > threshold) {</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  bound_flip_candidates->push_back(top.col);</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  std::pop_heap(breakpoints_.begin(), breakpoints_.end());</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  breakpoints_.pop_back();</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  }</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  }</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  }</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> </div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="comment">// TODO(user): We want to maximize both the ratio (objective improvement)</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// and the coeff_magnitude (stable pivot), so we have to make some</span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="comment">// trade-offs. Investigate alternative strategies.</span></div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">if</span> (top.coeff_magnitude >= best_coeff) {</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="comment">// Update harris_ratio. Note that because we process ratio in order, the</span></div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="comment">// harris ratio can only get smaller if the coeff_magnitude is bigger</span></div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="comment">// than the one of the best coefficient.</span></div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  harris_ratio = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  harris_ratio, top.ratio + harris_tolerance / top.coeff_magnitude);</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span> </div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="comment">// If the dual infeasibility is too high, the harris_ratio can be</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="comment">// negative. In this case we set it to 0.0, allowing any infeasible</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="comment">// position to enter the basis. This is quite important because its</span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="comment">// helps in the choice of a stable pivot.</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  harris_ratio =</div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(harris_ratio, minimum_delta / top.coeff_magnitude);</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">if</span> (top.coeff_magnitude == best_coeff && top.ratio == step) {</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <a class="code" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(*entering_col, <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  equivalent_entering_choices_.push_back(top.col);</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  equivalent_entering_choices_.clear();</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  best_coeff = top.coeff_magnitude;</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  *entering_col = top.col;</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span> </div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="comment">// Note that the step is not directly used, so it is okay to leave it</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="comment">// negative.</span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  step = top.ratio;</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  }</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> </div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="comment">// Remove the top breakpoint and maintain the heap structure.</span></div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="comment">// This is the same as doing a pop() on a priority_queue.</span></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  std::pop_heap(breakpoints_.begin(), breakpoints_.end());</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  breakpoints_.pop_back();</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  }</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// Break the ties randomly.</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">if</span> (!equivalent_entering_choices_.empty()) {</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  equivalent_entering_choices_.push_back(*entering_col);</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  *entering_col =</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  equivalent_entering_choices_[std::uniform_int_distribution<int>(</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  0, equivalent_entering_choices_.size() - 1)(random_)];</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <a class="code" href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a>(</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  stats_.num_perfect_ties.Add(equivalent_entering_choices_.size()));</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  }</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span> </div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">if</span> (*entering_col == <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">Status::OK</a>();</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> </div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="comment">// If best_coeff is small and they are potential bound flips, we can take a</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">// smaller step but use a good pivot.</span></div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> pivot_limit = parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#a68285ca7ffce0d4295c9ce20414eaec4">minimum_acceptable_pivot</a>();</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordflow">if</span> (best_coeff < pivot_limit && !bound_flip_candidates->empty()) {</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="comment">// Note that it is okay to leave more candidate than necessary in the</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="comment">// returned bound_flip_candidates vector.</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = bound_flip_candidates->size() - 1; i >= 0; --i) {</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keyword">const</span> ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = (*bound_flip_candidates)[i];</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">if</span> (std::abs(update_coefficient[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) < pivot_limit) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span> </div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <a class="code" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Used bound flip to avoid bad pivot. Before: "</span> << best_coeff</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  << <span class="stringliteral">" now: "</span> << std::abs(update_coefficient[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]);</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  *entering_col = <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  }</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  }</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span> </div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">Status::OK</a>();</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> }</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> </div><div class="line"><a name="l00230"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_entering_variable.html#aa271bff260917fd62d0d7509b7118ad6"> 230</a></span> <a class="code" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code" href="classoperations__research_1_1glop_1_1_entering_variable.html#aa271bff260917fd62d0d7509b7118ad6">EnteringVariable::DualPhaseIChooseEnteringColumn</a>(</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordtype">bool</span> nothing_to_recompute, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_update_row.html">UpdateRow</a>& update_row,</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> cost_variation, ColIndex* entering_col) {</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <a class="code" href="status_8h.html#ae9a90d3e61ffae636234f2c1283117d8">GLOP_RETURN_ERROR_IF_NULL</a>(entering_col);</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& update_coefficient = update_row.<a class="code" href="classoperations__research_1_1glop_1_1_update_row.html#a30fddb9e35865ba28420bd52538a183f">GetCoefficients</a>();</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& reduced_costs = reduced_costs_-><a class="code" href="classoperations__research_1_1glop_1_1_reduced_costs.html#a9f7d17ed171863f104fbb2a450f89251">GetReducedCosts</a>();</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <a class="code" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> </div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">// List of breakpoints where a variable change from feasibility to</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">// infeasibility or the opposite.</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  breakpoints_.clear();</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  breakpoints_.reserve(update_row.<a class="code" href="classoperations__research_1_1glop_1_1_update_row.html#af8e957f1c8389089554ded7bd2b7b45f">GetNonZeroPositions</a>().size());</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span> </div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> threshold = nothing_to_recompute</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  ? parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#a68285ca7ffce0d4295c9ce20414eaec4">minimum_acceptable_pivot</a>()</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  : parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#a802ffefaec0732058182bb426e8edbd2">ratio_test_zero_threshold</a>();</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> dual_feasibility_tolerance =</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  reduced_costs_-><a class="code" href="classoperations__research_1_1glop_1_1_reduced_costs.html#aa6a9551b792028d16dc7123c80f429d1">GetDualFeasibilityTolerance</a>();</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> harris_tolerance =</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#a40a2f57f5c801d77d6af1848383a4171">harris_tolerance_ratio</a>() * dual_feasibility_tolerance;</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> minimum_delta =</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  parameters_.<a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html#aad2c4edf11b93e46bae7f18ebd43301c">degenerate_ministep_factor</a>() * dual_feasibility_tolerance;</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> </div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_bitset64.html">DenseBitRow</a>& can_decrease = variables_info_.<a class="code" href="classoperations__research_1_1glop_1_1_variables_info.html#a71d4734d51e7037c043b68a74bd7857f">GetCanDecreaseBitRow</a>();</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_bitset64.html">DenseBitRow</a>& can_increase = variables_info_.<a class="code" href="classoperations__research_1_1glop_1_1_variables_info.html#a6cc56ab5da3a82aa2793d18a37f422c4">GetCanIncreaseBitRow</a>();</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">VariableTypeRow</a>& variable_type = variables_info_.<a class="code" href="classoperations__research_1_1glop_1_1_variables_info.html#a78146b251b30383686ec55362254cc3b">GetTypeRow</a>();</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  num_operations_ += 10 * update_row.<a class="code" href="classoperations__research_1_1glop_1_1_update_row.html#af8e957f1c8389089554ded7bd2b7b45f">GetNonZeroPositions</a>().size();</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : update_row.<a class="code" href="classoperations__research_1_1glop_1_1_update_row.html#af8e957f1c8389089554ded7bd2b7b45f">GetNonZeroPositions</a>()) {</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="comment">// Boxed variables shouldn't be in the update position list because they</span></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="comment">// will be dealt with afterwards by MakeBoxedVariableDualFeasible().</span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <a class="code" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(variable_type[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>], <a class="code" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a62e32b9a6efb029208f576ee123b459f">VariableType::UPPER_AND_LOWER_BOUNDED</a>);</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span> </div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="comment">// Fixed variable shouldn't be in the update position list.</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <a class="code" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(variable_type[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>], <a class="code" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103">VariableType::FIXED_VARIABLE</a>);</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="comment">// Skip if the coeff is too small to be a numerically stable pivot.</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">if</span> (std::abs(update_coefficient[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) < threshold) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> </div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="comment">// We will add ratio * coeff to this column. cost_variation makes sure</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="comment">// the leaving variable will be dual-feasible (its update coeff is</span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="comment">// sign(cost_variation) * 1.0).</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="comment">//</span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="comment">// TODO(user): This is the same in DualChooseEnteringColumn(), remove</span></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="comment">// duplication?</span></div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> coeff = (cost_variation > 0.0) ? update_coefficient[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  : -update_coefficient[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span> </div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="comment">// Only proceed if there is a transition, note that if reduced_costs[col]</span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="comment">// is close to zero, then the variable is counted as dual-feasible.</span></div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordflow">if</span> (std::abs(reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) <= dual_feasibility_tolerance) {</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="comment">// Continue if the variation goes in the dual-feasible direction.</span></div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keywordflow">if</span> (coeff > 0 && !can_decrease.<a class="code" href="classoperations__research_1_1_bitset64.html#aa454a4099ee887726b8f5b4a8ed1a81d">IsSet</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">if</span> (coeff < 0 && !can_increase.<a class="code" href="classoperations__research_1_1_bitset64.html#aa454a4099ee887726b8f5b4a8ed1a81d">IsSet</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="comment">// For an already dual-infeasible variable, we allow to push it until</span></div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="comment">// the harris_tolerance. But if it is past that or close to it, we also</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">// always enforce a minimum push.</span></div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">if</span> (coeff * reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] > 0.0) {</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  breakpoints_.push_back(ColWithRatio(</div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>,</div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(minimum_delta,</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  harris_tolerance - std::abs(reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>])),</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  std::abs(coeff)));</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  }</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="comment">// If the two are of the same sign, there is no transition, skip.</span></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">if</span> (coeff * reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] > 0.0) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  }</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span> </div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="comment">// We are sure there is a transition, add it to the set of breakpoints.</span></div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  breakpoints_.push_back(ColWithRatio(</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, std::abs(reduced_costs[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) + harris_tolerance, std::abs(coeff)));</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  }</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span> </div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="comment">// Process the breakpoints in priority order.</span></div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  std::make_heap(breakpoints_.begin(), breakpoints_.end());</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="comment">// Because of our priority queue, it is easy to choose a sub-optimal step to</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="comment">// have a stable pivot. The pivot with the highest magnitude and that reduces</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// the infeasibility the most is chosen.</span></div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> pivot_magnitude = 0.0;</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span> </div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="comment">// Select the last breakpoint that still improves the infeasibility and has a</span></div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="comment">// numerically stable pivot.</span></div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  *entering_col = <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>;</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> step = -1.0;</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> improvement = std::abs(cost_variation);</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keywordflow">while</span> (!breakpoints_.empty()) {</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keyword">const</span> ColWithRatio top = breakpoints_.front();</div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span> </div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="comment">// We keep the greatest coeff_magnitude for the same ratio.</span></div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(top.ratio > step ||</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  (top.ratio == step && top.coeff_magnitude <= pivot_magnitude));</div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="keywordflow">if</span> (top.ratio > step && top.coeff_magnitude >= pivot_magnitude) {</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  *entering_col = top.col;</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  step = top.ratio;</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  pivot_magnitude = top.coeff_magnitude;</div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  }</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  improvement -= top.coeff_magnitude;</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span> </div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="comment">// If the variable is free, then not only do we loose the infeasibility</span></div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="comment">// improvment, we also render it worse if we keep going in the same</span></div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="comment">// direction.</span></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">if</span> (can_decrease.<a class="code" href="classoperations__research_1_1_bitset64.html#aa454a4099ee887726b8f5b4a8ed1a81d">IsSet</a>(top.col) && can_increase.<a class="code" href="classoperations__research_1_1_bitset64.html#aa454a4099ee887726b8f5b4a8ed1a81d">IsSet</a>(top.col) &&</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  std::abs(reduced_costs[top.col]) > threshold) {</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  improvement -= top.coeff_magnitude;</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  }</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span> </div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keywordflow">if</span> (improvement <= 0.0) <span class="keywordflow">break</span>;</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  std::pop_heap(breakpoints_.begin(), breakpoints_.end());</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  breakpoints_.pop_back();</div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  }</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">Status::OK</a>();</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> }</div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> </div><div class="line"><a name="l00346"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_entering_variable.html#ae7202d055b6b172a8a1da4f5b136f9ea"> 346</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_entering_variable.html#ae7202d055b6b172a8a1da4f5b136f9ea">EnteringVariable::SetParameters</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_glop_parameters.html">GlopParameters</a>& <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>) {</div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  parameters_ = <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>;</div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span> }</div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span> </div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span> } <span class="comment">// namespace glop</span></div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span> } <span class="comment">// namespace operations_research</span></div><div class="ttc" id="alldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_update_row_html_a30fddb9e35865ba28420bd52538a183f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_update_row.html#a30fddb9e35865ba28420bd52538a183f">operations_research::glop::UpdateRow::GetCoefficients</a></div><div class="ttdeci">const DenseRow & GetCoefficients() const</div><div class="ttdef"><b>Definition:</b> <a href="update__row_8cc_source.html#l00165">update_row.cc:165</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_variables_info_html_a71d4734d51e7037c043b68a74bd7857f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_variables_info.html#a71d4734d51e7037c043b68a74bd7857f">operations_research::glop::VariablesInfo::GetCanDecreaseBitRow</a></div><div class="ttdeci">const DenseBitRow & GetCanDecreaseBitRow() const</div><div class="ttdef"><b>Definition:</b> <a href="variables__info_8cc_source.html#l00298">variables_info.cc:298</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_variables_info_html_a6cc56ab5da3a82aa2793d18a37f422c4"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_variables_info.html#a6cc56ab5da3a82aa2793d18a37f422c4">operations_research::glop::VariablesInfo::GetCanIncreaseBitRow</a></div><div class="ttdeci">const DenseBitRow & GetCanIncreaseBitRow() const</div><div class="ttdef"><b>Definition:</b> <a href="variables__info_8cc_source.html#l00294">variables_info.cc:294</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_afcaa7cadd41741bb855c2ada1d2ef927"><div class="ttname"><a href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a></div><div class="ttdeci">#define VLOG(verboselevel)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00983">base/logging.h:983</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_reduced_costs_html_aa6a9551b792028d16dc7123c80f429d1"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_reduced_costs.html#aa6a9551b792028d16dc7123c80f429d1">operations_research::glop::ReducedCosts::GetDualFeasibilityTolerance</a></div><div class="ttdeci">Fractional GetDualFeasibilityTolerance() const</div><div class="ttdef"><b>Definition:</b> <a href="reduced__costs_8h_source.html#l00177">reduced_costs.h:177</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a4452e21ffb34da40470f1e0791800027a62e32b9a6efb029208f576ee123b459f"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a62e32b9a6efb029208f576ee123b459f">operations_research::glop::VariableType::UPPER_AND_LOWER_BOUNDED</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_afb755b7934d8679476e2f05a89739bcd"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">operations_research::glop::kInvalidCol</a></div><div class="ttdeci">const ColIndex kInvalidCol(-1)</div></div>
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<div class="ttc" id="markowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00183">markowitz.cc:183</a></div></div>
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<div class="ttc" id="stats_8h_html_a9995704aaaf45fc21e08c847551a8d04"><div class="ttname"><a href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a></div><div class="ttdeci">#define SCOPED_TIME_STAT(stats)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00438">stats.h:438</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00078">lp_types.h:78</a></div></div>
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<div class="ttc" id="status_8h_html_ae9a90d3e61ffae636234f2c1283117d8"><div class="ttname"><a href="status_8h.html#ae9a90d3e61ffae636234f2c1283117d8">GLOP_RETURN_ERROR_IF_NULL</a></div><div class="ttdeci">#define GLOP_RETURN_ERROR_IF_NULL(arg)</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00087">status.h:87</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_status_html_a071b1d04197c0ac6e7a4d0ec0b91ff43"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">operations_research::glop::Status::OK</a></div><div class="ttdeci">static const Status OK()</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00056">status.h:56</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_entering_variable_html_afaf135d40c257d0f1a49aa8e795c9b03"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_entering_variable.html#afaf135d40c257d0f1a49aa8e795c9b03">operations_research::glop::EnteringVariable::DualChooseEnteringColumn</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status DualChooseEnteringColumn(bool nothing_to_recompute, const UpdateRow &update_row, Fractional cost_variation, std::vector< ColIndex > *bound_flip_candidates, ColIndex *entering_col)</div><div class="ttdef"><b>Definition:</b> <a href="entering__variable_8cc_source.html#l00033">entering_variable.cc:33</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_bitset64_html"><div class="ttname"><a href="classoperations__research_1_1_bitset64.html">operations_research::Bitset64< ColIndex ></a></div></div>
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<div class="ttc" id="timer_8h_html"><div class="ttname"><a href="timer_8h.html">timer.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_glop_parameters_html_aad2c4edf11b93e46bae7f18ebd43301c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_glop_parameters.html#aad2c4edf11b93e46bae7f18ebd43301c">operations_research::glop::GlopParameters::degenerate_ministep_factor</a></div><div class="ttdeci">double degenerate_ministep_factor() const</div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l02532">parameters.pb.h:2532</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_glop_parameters_html_a802ffefaec0732058182bb426e8edbd2"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_glop_parameters.html#a802ffefaec0732058182bb426e8edbd2">operations_research::glop::GlopParameters::ratio_test_zero_threshold</a></div><div class="ttdeci">double ratio_test_zero_threshold() const</div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l01577">parameters.pb.h:1577</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_variables_info_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_variables_info.html">operations_research::glop::VariablesInfo</a></div><div class="ttdef"><b>Definition:</b> <a href="variables__info_8h_source.html#l00055">variables_info.h:55</a></div></div>
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<div class="ttc" id="alldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_entering_variable_html_ae7202d055b6b172a8a1da4f5b136f9ea"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_entering_variable.html#ae7202d055b6b172a8a1da4f5b136f9ea">operations_research::glop::EnteringVariable::SetParameters</a></div><div class="ttdeci">void SetParameters(const GlopParameters &parameters)</div><div class="ttdef"><b>Definition:</b> <a href="entering__variable_8cc_source.html#l00346">entering_variable.cc:346</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_a46e69120fbd3b36e6960e096d23b66f0"><div class="ttname"><a href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a></div><div class="ttdeci">#define DCHECK_NE(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="namespaceoperations__research_1_1glop_html_a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103">operations_research::glop::VariableType::FIXED_VARIABLE</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_update_row_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_update_row.html">operations_research::glop::UpdateRow</a></div><div class="ttdef"><b>Definition:</b> <a href="update__row_8h_source.html#l00040">update_row.h:40</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_status_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html">operations_research::glop::Status</a></div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00026">status.h:26</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_variables_info_html_a78146b251b30383686ec55362254cc3b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_variables_info.html#a78146b251b30383686ec55362254cc3b">operations_research::glop::VariablesInfo::GetTypeRow</a></div><div class="ttdeci">const VariableTypeRow & GetTypeRow() const</div><div class="ttdef"><b>Definition:</b> <a href="variables__info_8cc_source.html#l00286">variables_info.cc:286</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_variables_info_html_a505af340486fcf70ee83abb32e31a628"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_variables_info.html#a505af340486fcf70ee83abb32e31a628">operations_research::glop::VariablesInfo::GetNonBasicBoxedVariables</a></div><div class="ttdeci">const DenseBitRow & GetNonBasicBoxedVariables() const</div><div class="ttdef"><b>Definition:</b> <a href="variables__info_8cc_source.html#l00312">variables_info.cc:312</a></div></div>
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<div class="ttc" id="port_2proto__utils_8h_html"><div class="ttname"><a href="port_2proto__utils_8h.html">proto_utils.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_update_row_html_af8e957f1c8389089554ded7bd2b7b45f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_update_row.html#af8e957f1c8389089554ded7bd2b7b45f">operations_research::glop::UpdateRow::GetNonZeroPositions</a></div><div class="ttdeci">const ColIndexVector & GetNonZeroPositions() const</div><div class="ttdef"><b>Definition:</b> <a href="update__row_8cc_source.html#l00167">update_row.cc:167</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_entering_variable_html_aa271bff260917fd62d0d7509b7118ad6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_entering_variable.html#aa271bff260917fd62d0d7509b7118ad6">operations_research::glop::EnteringVariable::DualPhaseIChooseEnteringColumn</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status DualPhaseIChooseEnteringColumn(bool nothing_to_recompute, const UpdateRow &update_row, Fractional cost_variation, ColIndex *entering_col)</div><div class="ttdef"><b>Definition:</b> <a href="entering__variable_8cc_source.html#l00230">entering_variable.cc:230</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_strict_i_t_i_vector_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">operations_research::glop::StrictITIVector< ColIndex, Fractional ></a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_glop_parameters_html_a68285ca7ffce0d4295c9ce20414eaec4"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_glop_parameters.html#a68285ca7ffce0d4295c9ce20414eaec4">operations_research::glop::GlopParameters::minimum_acceptable_pivot</a></div><div class="ttdeci">double minimum_acceptable_pivot() const</div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l01661">parameters.pb.h:1661</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_ae17f8119c108cf3070bad3449c7e0006"><div class="ttname"><a href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a></div><div class="ttdeci">#define DCHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00889">base/logging.h:889</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_reduced_costs_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_reduced_costs.html">operations_research::glop::ReducedCosts</a></div><div class="ttdef"><b>Definition:</b> <a href="reduced__costs_8h_source.html#l00049">reduced_costs.h:49</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_bitset64_html_aa454a4099ee887726b8f5b4a8ed1a81d"><div class="ttname"><a href="classoperations__research_1_1_bitset64.html#aa454a4099ee887726b8f5b4a8ed1a81d">operations_research::Bitset64::IsSet</a></div><div class="ttdeci">bool IsSet(IndexType i) const</div><div class="ttdef"><b>Definition:</b> <a href="bitset_8h_source.html#l00485">bitset.h:485</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_entering_variable_html_a2dbed549d25654617b466ea86d51fa51"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_entering_variable.html#a2dbed549d25654617b466ea86d51fa51">operations_research::glop::EnteringVariable::EnteringVariable</a></div><div class="ttdeci">EnteringVariable(const VariablesInfo &variables_info, absl::BitGenRef random, ReducedCosts *reduced_costs)</div><div class="ttdef"><b>Definition:</b> <a href="entering__variable_8cc_source.html#l00025">entering_variable.cc:25</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="entering__variable_8h_html"><div class="ttname"><a href="entering__variable_8h.html">entering_variable.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_variables_info_html_a611fb1da73c33e2716b380db980fa825"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_variables_info.html#a611fb1da73c33e2716b380db980fa825">operations_research::glop::VariablesInfo::GetBoundDifference</a></div><div class="ttdeci">Fractional GetBoundDifference(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="variables__info_8h_source.html#l00141">variables_info.h:141</a></div></div>
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<div class="ttc" id="cp__model__fz__solver_8cc_html_a10a1eab179b472c030bdc2a2efef7219"><div class="ttname"><a href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a></div><div class="ttdeci">SatParameters parameters</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__fz__solver_8cc_source.html#l00120">cp_model_fz_solver.cc:120</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_reduced_costs_html_a9f7d17ed171863f104fbb2a450f89251"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_reduced_costs.html#a9f7d17ed171863f104fbb2a450f89251">operations_research::glop::ReducedCosts::GetReducedCosts</a></div><div class="ttdeci">const DenseRow & GetReducedCosts()</div><div class="ttdef"><b>Definition:</b> <a href="reduced__costs_8cc_source.html#l00319">reduced_costs.cc:319</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_glop_parameters_html_a40a2f57f5c801d77d6af1848383a4171"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_glop_parameters.html#a40a2f57f5c801d77d6af1848383a4171">operations_research::glop::GlopParameters::harris_tolerance_ratio</a></div><div class="ttdeci">double harris_tolerance_ratio() const</div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l01605">parameters.pb.h:1605</a></div></div>
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<div class="ttc" id="lp__data_2lp__utils_8h_html"><div class="ttname"><a href="lp__data_2lp__utils_8h.html">lp_utils.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_glop_parameters_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_glop_parameters.html">operations_research::glop::GlopParameters</a></div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l00194">parameters.pb.h:194</a></div></div>
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<div class="ttc" id="stats_8h_html_a3c3e6b102f0d91c523099325c98e1887"><div class="ttname"><a href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a></div><div class="ttdeci">#define IF_STATS_ENABLED(instructions)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00437">stats.h:437</a></div></div>
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