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Re: Matrix Minimization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99805] Re: Matrix Minimization
  • From: Paul <pnorthug at gmail.com>
  • Date: Fri, 15 May 2009 04:17:23 -0400 (EDT)
  • References: <gue2j0$7kd$1@smc.vnet.net> <gugaqf$egm$1@smc.vnet.net>

On May 14, 8:05 am, "math.mud.mad" <math.mud.... at gmail.com> wrote:
> On May 14, 2:39 pm, dh <d... at metrohm.com> wrote:
>
>
>
> > Hi,
>
> > you may minimize a real scalar but not a matrix. However, what you can
>
> > do is to minimize some measure like a Norm of the matrix.
>
> > Towards this aim, you will have to calculate e.g. Norm[] and then
>
> > minimize it.
>
> > Daniel
>
> > math.mud.... at gmail.com wrote:
> > > Hi ,
>
> > > i would like to minimize the following matrix  M with respect to A.
>
> > > M=  E_X + A E_S A' + A E_P A'        E_X H' +A E_S H'
> > >        H E_X + H E_S A'                 H E_X=
 H=
> ' + H E_S H' + E_Q
>
> > > where E_X, E_S, E_P and E_Q are covariance matrices..
>
> > > can we do matrix optimization in mathematica?
>
> > > thanks a lot..
>
> Hi Daniel,
>
> sorry for my mistake. i want to optimize log det (M) with respect to
> A. can i use mathematica for that?
>
> regards,

I think log det is concave (maybe only on the positive semidefinite
cone, don't remember). You may want to just calculate the gradient and
use one of the standard FindMaximize methods with bfgs or conjugate
gradient. This is not the best way to solve the problem (see Boyd and
Vanderberghe) but may work.

P=E5l


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