<div dir="ltr">I fixed it partially. The derivative of the p-norm doesn't exist at zero so I had to be careful with that. I also introduced a scale factor for the objective function before the penalty term. This way the convergence is faster and inf_du is more reasonable. The problem is that I'm not able to reach the same minima I was achieving before, which is better than the one I have now. If I change that scale factor to a number between 5 and 10, the inf_du goes nuts again.<br></div><div class="gmail_extra"><br><div class="gmail_quote">On Fri, Mar 13, 2015 at 10:03 AM, Miguel Angel Salazar de Troya <span dir="ltr"><<a href="mailto:salazardetroya@gmail.com" target="_blank">salazardetroya@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Thanks for your response. My objective function is a double p-norm. I have a solid mechanics problem in time and space and I want to get the maximum value of a quantity over time and space, hence the double p-norm with a high p coefficient (14). My variables are the material properties. Something like topology optimization, but just at specific locations. The variables change from 0.001 to 1. It's 0.001 to avoid singularities in the simulation.<div><br></div><div>I get such a high dual infeasibility when my initial values are 0.5 and the problem is unconstrained (although I have the penalty function to drive the solution to a 0.001-1 layout) Imposing a volume constraint (making the sum of the variables equal to a certain value) doesn't result in such a high dual infeasibility, although still high (~1e9). For the unconstrained case, starting with an initial value different than 0.5 results in an inf_du value around 1e6. Also important, if a variable's initial value is less than 0.5, the optimal value will be always 0, if it is greater than 0.5, the optimal value will be always 1. The gradient of the objective function without the penalty term is of the order of 1e-2 for all the variables. Is the penalty term dominating the convergence because of this? If I scale the objective function before applying the penalty term I will get better results?</div><span class="HOEnZb"><font color="#888888"><div><br></div><div>Miguel</div></font></span><div><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Mar 12, 2015 at 2:52 PM, Greg Horn <span dir="ltr"><<a href="mailto:gregmainland@gmail.com" target="_blank">gregmainland@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Your dual infeasibility is off the charts. Something is really off. It would help if you describe your problem more, or give a similar problem.<br></div><br><div class="gmail_quote"><div><div>On Tue, Mar 10, 2015 at 8:05 PM Miguel Angel Salazar de Troya <<a href="mailto:salazardetroya@gmail.com" target="_blank">salazardetroya@gmail.com</a>> wrote:<br></div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div><div dir="ltr">Hi<div><br></div><div>I'm trying to optimize an unconstrained problem with a penalty function. My goal is to obtain either 0 or 1 for the variables and the penalty term takes care of this. </div><div><br></div><div>The optimization eventually converges, but at the beginning, for each iteration, the objective function is evaluated many times, over 50 times. For each iteration, I obtain an output like this:</div><div><br></div><div>iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls<br></div><div><div> 5 1.4656145e+04 0.00e+00 1.29e+53 -0.1 8.80e+92 -5.4 8.88e-95 2.08e-148f172 FqsWSWs</div><div><br></div><div>Any idea of what's going on and how I could make it converge faster?</div><div><br></div><div>Thanks in advance</div><div>Miguel</div><div><br></div>-- <br><div><div dir="ltr"><font face="verdana, sans-serif"><b>Miguel Angel Salazar de Troya</b></font><span><font color="#888888"><br><font face="arial,helvetica,sans-serif">Graduate Research Assistant<br>Department of Mechanical Science and Engineering<br></font>University of Illinois at Urbana-Champaign<br>(217) 550-2360<br>
<a href="mailto:salaza11@illinois.edu" target="_blank">salaza11@illinois.edu</a></font></span><div><br></div></div></div>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div><div dir="ltr"><font face="verdana, sans-serif"><b>Miguel Angel Salazar de Troya</b></font><span><font color="#888888"><br><font face="arial,helvetica,sans-serif">Graduate Research Assistant<br>Department of Mechanical Science and Engineering<br></font>University of Illinois at Urbana-Champaign<br>(217) 550-2360<br>
<a href="mailto:salaza11@illinois.edu" target="_blank">salaza11@illinois.edu</a></font></span><div><br></div></div></div>
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</blockquote></div><br><br clear="all"><br>-- <br><div class="gmail_signature"><div dir="ltr"><font face="verdana, sans-serif"><b>Miguel Angel Salazar de Troya</b></font><span><font color="#888888"><br><font face="arial,helvetica,sans-serif">Graduate Research Assistant<br>Department of Mechanical Science and Engineering<br></font>University of Illinois at Urbana-Champaign<br>(217) 550-2360<br>
<a href="mailto:salaza11@illinois.edu" target="_blank">salaza11@illinois.edu</a></font></span><div><br></div></div></div>
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