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Re: FindMinimum to minimize e . w . e

Albert Maydeu-Olivares wrote:

> I have a couple of questions regarding the GLS fitting function
> grad=-2e . w. j;
> f1=FindMinimum[e . w . e,Evaluate[Sequence@@startval],Gradient->grad]
> where e is symbolic vector and w is a matrix of constants.

Have you had a look at the Calculus`VariationalMethods` package?
NVariationalBound effectively does this computation and uses FindMinimum

> 1) when I try to update w at each iteration as
> w:=Inverse[symbolic matrix];
> f2=FindMinimum[e . w . e,Evaluate[Sequence@@startval],Gradient->grad];
> it takes forever. I suspect that the reason is that at each iteration
> Mathematica uses
> (e. w . e)/. rule        which takes about 34 sec on my machine, instead of
> (e/.rule) . Inverse[symbolic matrix/.rule] . (e/.rule)        .11 sec

I'm sure that there is a way of re-writing your example to work in this way but

it is not easy to explain how to do this in general because it could depend
on the problem specifics.

> 2) Minimizing f1 is equivalent to minimizing
> f3=FindMinimum[Tr[MatrixPower[mat1 . (mat2 -mat3) ,2]],Gradient->gradient,
>     Evaluate[Sequence@@startval]]
> where mat1 and mat2 are numerical matrices, and mat3 is symbolic. I'm
> interested in f3 because it's supposed to be faster. However, Mathematica 3
> gives me an error
> FindMinimum::"fdss": Gradient->...
>     "Search specification should be a list with 2-4 elements."
> yet Tr[MatrixPower[mat1 . (mat2 -mat3) ,2]]/.rule and gradient/.rule work
> fine. What may be happening?

You have defined Tr?

Perhaps a Notebook with a specific (simple) example would make
this all clear?

Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at

            God IS a weakly left-handed dice player

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