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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Hi Filippo,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">As far as I am aware, both IPOPT and BONMIN treat
</span>N \leq \sum{i\in I}v_i \leq N<span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"> as
</span>\sum{i\in I}v_i=N<span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">. Therefore you are correctly implementing an equality constraint. Using OPTI, you can check this using IPOPT (relax all integer
variables) and checking the display output of IPOPT – it should state that it found your equality constraint:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">This is Ipopt version 3.12.3, running with linear solver pardiso.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Number of nonzeros in equality constraint Jacobian...: 2<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Number of nonzeros in inequality constraint Jacobian.: 2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Number of nonzeros in Lagrangian Hessian.............: 3<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Total number of variables............................: 2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"> variables with only lower bounds: 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"> variables with lower and upper bounds: 2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"> variables with only upper bounds: 0<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Total number of equality constraints.................: 1<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Total number of inequality constraints...............: 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"> inequality constraints with only lower bounds: 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"> inequality constraints with lower and upper bounds: 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"> inequality constraints with only upper bounds: 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">You may also increase the print out of BONMIN above the default, so each IPOPT solve is displayed. See test_bonmin_linearcon.m line
67, increase this to 4, and you will see what I mean. This option is not available via the OPTI object however.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Regarding the convergence issues, this is best left to one of the members of this forum to discuss the reasons this could be occurring.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Jonathan<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext"> bonmin-bounces@list.coin-or.org
[mailto:bonmin-bounces@list.coin-or.org] <b>On Behalf Of </b>Filippo Pecci<br>
<b>Sent:</b> Friday, 15 May 2015 1:07 a.m.<br>
<b>To:</b> bonmin@list.coin-or.org<br>
<b>Subject:</b> [Bonmin] Issues when dealing with linear constraints involving integer variables<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal" style="margin-bottom:12.0pt">Dear all,<br>
<br>
We have been using BONMIN to solve some MINLP problems with binary integers that represent ON/OFF type elements in our optimization. One of the linear constraints we have is a that the sum of integer variables is a fixed positive integer N (i.e. \sum{i\in
I}v_i=N)<o:p></o:p></p>
<ul type="disc">
<li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
We use bonmin through OPTI's mex interface. As a result, we implement this linear constraint on the integer variable as N \leq \sum{i\in I}v_i \leq N. This has some convergence issues, often failing to find a feasible solution.<o:p></o:p></li></ul>
<ul type="disc">
<li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1 level1 lfo2">
We relaxed the above constraints using small delta to N-\delta \leq \sum{i\in I}v_i \leq N+\delta. Although this solved the issue for some small N, the same problem was faced for larger N values.<o:p></o:p></li></ul>
<ul type="disc">
<li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l2 level1 lfo3">
We also replaced this constraint with \sum{i\in I}v_i \leq N, which is equivalent to the original constraint in our problem since the objective function cannot be improved with less ON elements (i.e. with less v_i that are equal to 1). This formulation always
works with good convergence properties.<o:p></o:p></li></ul>
<p class="MsoNormal"><br>
What is it about bonmin that causes this behaviour? Pseudocosts? How bonmin passes equality constraints in integer variables to ipopt? Can it be related to the branching rules?<br>
<br>
Thank you for your time and consideration.<br>
<br>
Best regards,<br>
<br>
Filippo Pecci <o:p></o:p></p>
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