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<p>Hi All,</p>
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<p>I have modeled a convex nonlinear problem using Bonmin's c++ interface. </p>
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<p>The problem also has absolute value constraints of the following format,</p>
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<p> <span style="font-family: "Courier New",monospace;">abs(x[i]-x[j]) > threshold</span></p>
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<p>I have modeled these absolute value constraints using the Big M approach and have introduced integer variables as below:</p>
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<p><span style="font-family: "Courier New",monospace;"> x[i]-x[j] + M*B > threshold and</span></p>
<p><span style="font-family: "Courier New",monospace;"> -x[i] +x[j] +M*(1-B) > threshold</span></p>
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<p>where M is a large value (based on my problem and not random) and B is the newly introduced binary/integer variable ( Have tried both approaches).</p>
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<p>While using a branch and bound algorithm, I printed the variable values for a particular iteration and see that the integer/binary variables have the values like below.</p>
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<p> <span style="font-family: "Courier New",monospace;">x[20]= 0.229109</span></p>
<p><span style="font-family: "Courier New",monospace;"> x[109]= 0.254611</span></p>
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<p>due to which the trial point which seems to be the best is being rejected due to in- feasibility and the algorithm exits stating that my problem is infeasible ( which is obvious if the integer/binary variables are varied continuously)
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<p>I even tried changing the option integer_tolerance as below</p>
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<p> <span style="font-family: "Courier New",monospace;">bonmin.options()->SetIntegerValue("bonmin.integer_tolerance",1);</span></p>
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<p>which by default is 1e-06 but is not respected by the solver.</p>
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<p>Could anyone comment if I am missing something or using a faulty model.</p>
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<p>Thanks in advance for your help.</p>
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<p>I can furnish more details of my problem if required. </p>
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<p>Thanks and Regards,<br>
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<div style="font-family:Tahoma; font-size:13px"><font size="4" face="Verdana">Ujwal Ramesh</font>
<div><font size="2" face="Verdana">Graduate Student,</font></div>
<div><font size="2" face="Verdana">University Of Cincinnati</font></div>
<div><font size="2" face="Verdana">Ph: +1-513-302-4771</font></div>
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