Math Forum Discussions

J

Posts: 9
Registered: 8/29/09

Re: LMI-toolbox vs YALMIP vs CVX
Posted: Aug 31, 2009 8:03 AM

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Very cool, Johan. I will install Yalmip and get some results by Tues. I'll let you know how it turns out. Thanks again for your help.

-JH

Johan Löfberg <loefberg@control.ee.ethz.ch> wrote in message <24563a55-24cc-4baf-bb0f-a397af54df44@j9g2000vbp.googlegroups.com>...
> Yp = sdpvar(n);
> Xp = sdpvar(n);
> Ac = sdpvar(n);
> Bc = sdpvar(n,p,'full');
> Cc = sdpvar(m,n,'full');
> Dc = sdpvar(p,p,'full');
>
> %Messy version where you have to keep track of zeros etc
> Constraints = [Yp > 0, Xy > 0];
> Constraints = [Constraints, [Yp eye(n) zeros(?,?) (Ap*Yp+Bb*Cc)' ...]
> >0]
> solvesdp(constraints)
>
> % Maybe easier, YALMIP will auto-complete to symmetric matrix and try
> to
> % find out dimensions of the zeros
> % http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?n=Commands.Blkvar
> Z = blkvar;
> Z(1,1) = Yp;
> Yp(2,1) = eye(n);
> Yp(3,1) = (Ap*Yp+Bb*Cc)';
> Yp(4,1) = Ac;
> Yp(5,1) = Cz*Yp+Db*CC;
> Yp(2,2) = Xy;
> etc...
> Constraints = [Yp > 0, Xy > 0, Z>0];
> solvesdp(constraints)
>
> email if you have any problems.
>
>
> On Aug 30, 10:00?pm, "JH " <jhl...@colorado.edu> wrote:
> > Johan L?fberg <loefb...@control.ee.ethz.ch> wrote in message <74d7b204-23c3-4f86-ba2c-ed0f4141d...@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- Hide quoted text -
> >
> > - Show quoted text -