<div dir="ltr"><div><div><div><div><div><br></div>Hi Chivalry,<br><br></div>a similar case occurs when solving structured support vector machines (structured SVMs), and the most efficient methods there used to be dual active set QP solvers, customly written for these problems.<br><br></div>However, recent literature has shown that the Frank-Wolfe method is quite efficient for these type of QPs.<br><br>See, e.g.<br> <a href="http://jmlr.csail.mit.edu/proceedings/papers/v28/lacoste-julien13-supp.pdf">http://jmlr.csail.mit.edu/proceedings/papers/v28/lacoste-julien13-supp.pdf</a><br></div>and the accompanying code<br> <a href="https://github.com/ppletscher/BCFWstruct">https://github.com/ppletscher/BCFWstruct</a><br><br></div><div>If your problem is of similar type, these methods are worth a try. If not, maybe you want to investigate whether they can be adapted to your type of problem.<br></div><div>(Structured SVMs are an important problem in machine learning and it took a few years until we could reliably solve these problems.)<br><br></div>Sebastian<br><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Fri, May 8, 2015 at 4:04 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">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>
<div style="color:rgb(0,0,0);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>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" target="_blank">nowozin@gmail.com</a>> wrote:</div><br><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" target="_blank">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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