Math Forum Discussions

J

Posts: 9
Registered: 8/29/09

Re: LMI-toolbox vs YALMIP vs CVX
Posted: Aug 30, 2009 4:00 PM

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Johan Löfberg <loefberg@control.ee.ethz.ch> wrote in message <74d7b204-23c3-4f86-ba2c-ed0f4141dd38@d23g2000vbm.googlegroups.com>...
> On Aug 29, 7:17?pm, "JH " <jhl...@colorado.edu> wrote:
> > Hello everyone-
> >
> > I have been having problems with the LMI-toolbox feasp not being able to find a feasible solution when there is one and also with mincx returning a solution that it thinks is feasible when the returned solution is in fact not feasible. ?So, I am thinking about trying some of the other package such as CVX and YALMIP.
> >
> > Has anyone had similar problems or had experience with some of the other (publicly) available packages that would indicate they are more robust/better than the LMI-toolbox?
> >
> > Thanks!
> > -JH
>
> For a general problem, you are much better off using a modern solver
> such sedumi or sdpt3, which are interfaced in YALMIP. Installing some
> of these solvers takes a couple of minutes and cost you nothing, so
> why not give them a try together with yalmip or cvx. In addition, you
> get a modelling language which will make it very easy to actually
> define the problems.
>
> Of course, I am slightly biased, being the developer of YALMIP :-)
>
> Just email me if you have any direct questions.
> /johan

Thanks for the reply, Johan.

I am working on a discrete time Hinf optimization LMI. Would there be an example of how to code up something that looks like (sorry, no matter how I try, the newsgroup interface is going to mangle the following):

N N Nw N N N Nz
------------------------------------------------------------------------------------------------
0 < [ Yp * * * * * *
I Xy * * * * *
0 0 Iw * * * *
Ap*Yp+Bb*Cc Ap+Bb*Dc*Cy Ba+Bb*Dc*Dy Yp * *
Ac Xy*Ap+Bc*Cy Xy*Ba+Bc*Dy I Xy *
Cz*Yp+Db*CC Cz+Db*Dc*Cy Da+Db*Dc*Dy 0 0 sigma*Iz ]

Yp, Xy are symmetric >0 & Ac,Bc,Cc,Dc are arbitrary rectangular and all other quantities are constants of appropriate dimensions-- dimensions are along the top.

The LMI-toolbox ususally finds a good solution until the dimension "N" becomes large enough, then it fails when there is in fact a solution.

CVX has not been successful yet-- it quits while the matrix has negative eigenvalues. Though, it is possible that I have made a mistake in coding it up.

I am going to try Yalmip next. It would be great if there was an example of coding up a similar, block-type LMI.

Thanks,
-JH