[Ipopt] IPOpt for l1 optimization?

[Andreas Waechter]

And with the linear constraints all together this will be an LP, so you 
will probably be best off with an LP solver rather than a general NLP 
solver.

Andreas Waechter

Associate Professor
Department of Industrial Engineering and Management Sciences
McCormick School of Engineering
Northwestern University
Evanston, IL 60208
USA


On 04/11/2012 01:29 PM, Frank E. Curtis wrote:
> min |x|
>
> is equivalent to
>
> min y
> s.t. -y <= x <= y, y >= 0
>
> and equivalent to
>
> min y + z
> s.t. x = y - z, (y,z) >= 0
>
> The latter two are smooth constrained problems.
>
> Frank E. Curtis
> P. C. Rossin Assistant Professor
> Industrial and Systems Engineering
> Lehigh University
> http://coral.ie.lehigh.edu/~frankecurtis 
> <http://coral.ie.lehigh.edu/%7Efrankecurtis>
>
>
> On Wed, Apr 11, 2012 at 2:00 PM, Frank Kampas <fkampas at msn.com 
> <mailto:fkampas at msn.com>> wrote:
>
>     I think the technique in question is sometimes referred to as
>     "goal programming".
>
>     -----Original Message----- From: Paul van Hoven
>     Sent: Wednesday, April 11, 2012 1:51 PM
>     To: Peter Carbonetto
>     Cc: ipopt at list.coin-or.org <mailto:ipopt at list.coin-or.org>
>     Subject: Re: [Ipopt] IPOpt for l1 optimization?
>
>
>     Thank you for the answer Peter. Can you recommend some sources on this
>     topic of transformation?
>
>     Am 11. April 2012 18:33 schrieb Peter Carbonetto
>     <pcarbo at uchicago.edu <mailto:pcarbo at uchicago.edu>>:
>
>         Is there an absolute value in that objective function you are
>         minimizing? If
>         so, then the answer is no, because the objective is non-smooth
>         (it has
>         undefined derivatives at zeros). But you can convert this to
>         an equivalent
>         smooth optimization problem with additional inequality
>         constraints. There is
>         quite a bit of literature on this topic.
>
>         Peter Carbonetto, Ph.D.
>         Postdoctoral Fellow
>         Dept. of Human Genetics
>         University of Chicago
>
>
>         On Wed, 11 Apr 2012, Paul van Hoven wrote:
>
>             I've got the following problem:
>
>             min_x sum_{i=1}^N | <x,c_i> |
>             s.t. Ax < 0
>
>             <x,c_i> denotes the standard scalar product between x and c_i.
>
>             Is this a problem that can be solved appropriately with IPOpt?
>             _______________________________________________
>             Ipopt mailing list
>             Ipopt at list.coin-or.org <mailto:Ipopt at list.coin-or.org>
>             http://list.coin-or.org/mailman/listinfo/ipopt
>
>
>     _______________________________________________
>     Ipopt mailing list
>     Ipopt at list.coin-or.org <mailto:Ipopt at list.coin-or.org>
>     http://list.coin-or.org/mailman/listinfo/ipopt
>     _______________________________________________
>     Ipopt mailing list
>     Ipopt at list.coin-or.org <mailto:Ipopt at list.coin-or.org>
>     http://list.coin-or.org/mailman/listinfo/ipopt
>
>
>
>
> _______________________________________________
> Ipopt mailing list
> Ipopt at list.coin-or.org
> http://list.coin-or.org/mailman/listinfo/ipopt
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.coin-or.org/pipermail/ipopt/attachments/20120411/aa9baf70/attachment.html>