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<p class="MsoNormal">Hi,</p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I’m using CBC 2.10.3 to solve the attached small MIQP (MIP with quad objective), but the solution is reported as “Integer infeasible”, which is not correct.
</p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The actual solution is x1=1, x2=1, with obj value -7.5. Continuous relaxation solution is x1 = 0.66, x2 = 1.333 with obj value -8.22222. See
<a href="https://www.inverseproblem.co.nz/OPTI/index.php/Probs/MIQP">https://www.inverseproblem.co.nz/OPTI/index.php/Probs/MIQP</a>
</p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The command I use is </p>
<p class="MsoNormal" style="text-indent:.5in"><b>cbc -import testmiqp.mps -minimize -solve -solution sol.txt<o:p></o:p></b></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The output shows interesting lines:<o:p></o:p></p>
<p class="MsoNormal"> […]<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Clp0000I Optimal - objective value -7.5<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Cbc0012I Integer solution of -7.5 found by feasibility pump after 0 iterations and 0 nodes (0.00 seconds)<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Cbc0001I Search completed - best objective -7.5, took 0 iterations and 0 nodes (0.00 seconds)<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Clp0006I 0 Obj -7.5<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Clp0000I Optimal - objective value -7.5<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">obj -7.5<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><b>Continuous objective value is -9</b> - 0.00 seconds<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Testing OsiObject options 0<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Cbc0006I The LP relaxation is infeasible or too expensive<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">[…]<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">So Feasibility Pump finds the integer solution with obj value -7.5, but then reported Continuous objective value of -9 seems incorrect.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">How can I solve this MIQP with cbc?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Many thanks for any help.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Jan-Willem<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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