[Ipopt] solving non-smooth large scale problem using ipopt

[key01023 at gmail.com]

Oh, this is great, thank you for informing me about this:D

With regards,
Chivalry

On May 8, 2015, at 11:13 AM, Sebastian Nowozin <nowozin at gmail.com> wrote:

> 
> Hi Chivalry,
> 
> 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.
> 
> However, recent literature has shown that the Frank-Wolfe method is quite efficient for these type of QPs.
> 
> See, e.g.
>     http://jmlr.csail.mit.edu/proceedings/papers/v28/lacoste-julien13-supp.pdf
> and the accompanying code
>     https://github.com/ppletscher/BCFWstruct
> 
> 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.
> (Structured SVMs are an important problem in machine learning and it took a few years until we could reliably solve these problems.)
> 
> Sebastian
> 
> 
> On Fri, May 8, 2015 at 4:04 PM, key01023 at gmail.com <key01023 at gmail.com> wrote:
> Hi Sebastian,
> 
> Thank you for your reply.
> 
> 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.
> 
> With regards,
> Chivalry
> 
> On May 8, 2015, at 10:57 AM, Sebastian Nowozin <nowozin at gmail.com> wrote:
> 
>> 
>> Hi Chivalry,
>> 
>> convex + non-smooth problems often originate from minimizing the maximum of multiple smooth convex problems.
>> 
>> 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.
>> The resulting instance is a smooth convex problem with convex constraints and as such amenable using IpOpt.
>> 
>> Sebastian
>> 
>> On Fri, May 8, 2015 at 3:45 PM, key01023 at gmail.com <key01023 at gmail.com> wrote:
>> Dear all,
>> 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.
>> 
>> With regards,
>> Chivalry
>> 
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>> http://list.coin-or.org/mailman/listinfo/ipopt
>> 
>> 
> 
> 

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