<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;">Hi Sebastian,<div><br></div><div>Thank you for your reply.</div><div><br></div><div>Yes, we indeed have maximum of multiple linear functions. However, the multiple is about 2^80 many such linear functions. However, I have a way to walk around without enumerating all such linear functions and provide a oracle to objective function values and sub gradient value. Do you think it is still possible to use IPopt to solve it? Thank you.</div><div><br><div apple-content-edited="true">
<div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;">With regards,<br>Chivalry</div>
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<br><div><div>On May 8, 2015, at 10:57 AM, Sebastian Nowozin <<a href="mailto:nowozin@gmail.com">nowozin@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div dir="ltr"><div><div><div><div><br></div>Hi Chivalry,<br><br></div>convex + non-smooth problems often originate from minimizing the maximum of multiple smooth convex problems.<br></div><br>If this is the case in your instance, you can reformulate the problem by introducing additional variables containing the individual objective function values, and a set of inequality constraints.<br></div><div>The resulting instance is a smooth convex problem with convex constraints and as such amenable using IpOpt.<br></div><div><br></div>Sebastian<br></div><div class="gmail_extra"><br><div class="gmail_quote">On Fri, May 8, 2015 at 3:45 PM, <a href="mailto:key01023@gmail.com">key01023@gmail.com</a> <span dir="ltr"><<a href="mailto:key01023@gmail.com" target="_blank">key01023@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 style="word-wrap:break-word"><div>Dear all,</div><div>I have a large class of non smooth convex optimization problems with about 8000 dimensions and I am looking for c++ solvers to solve that. I tried level method (extremely slow due to built up of sub-gradients), optimal gradient method due to Nesterov (very slow convergence), limited memory bundle method (LMBM) (no compilable solver available, failed to compile LMBM). I want to ask whether ipopt can be applied to solve this problem, because it uses limited memory BFGS which i guess somewhat resembles the LMBM methods. If so, is there some c++ file examples showing a case where we don’t need to provide the Hessian. Thank you.</div><br><div>
<div style="letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; word-wrap: break-word;">With regards,<br></div><div style="letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; word-wrap: break-word;">Chivalry</div></div></div><br>_______________________________________________<br>
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