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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Dear all,<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I am using IpOpt in MATLAB (through a mex file) to solve a large-scale optimization problem where we estimate the gradient and jacobian with finite differences.<o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal>The problem is that there are times when IpOpt worsens the obj function value than the earlier iterates and sometimes, it even makes the iterates infeasible (although the earlier iterates were feasible). Beyond that point it goes into a restoration mode: it tries remove the constraint violation first and then tries to improve the objective function. The net result is that it starts at some obj function value and reaches the same value again after some time – the time seems to be spent on correcting the constraint violation that wasn’t there earlier. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I am not able to explain this behavior. Any suggestions/thoughts on why this is happening will be really helpful.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Here are some of my thoughts which may be helpful to reach a reasonable conclusion:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>1) Could it be because we are using finite differences to estimate the gradients? Especially because we are using a straightforward expression based on the forward difference method with a small constant perturbation to evaluate the gradient. While one would expect sensitivity to gradient accuracy, I’m not sure if it should affect to this extent.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>2) Let us just say the current IpOpt iterate is somehow worse than the earlier iterate. Why doesn’t IpOpt have an internal mechanism by which it goes back to the earlier iterate and tries again; or some variant thereof? If it does that already, then why does that not seem to be the case – it seems to be printing out the iterates irrespective of whether they are better/worse than the earlier ones.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Thank you so much for your time and help. Any thoughts/insights/suggestions will be highly appreciated.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Regards,<o:p></o:p></p><p class=MsoNormal>-kedar.<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></div></body></html>