Matrix trace minimization and zeros

[GoodSpirit]

Hello, :)

I would like to minimize and find the zeros of the function F(S,P)=trace(S-SP’(A+ PSP’)^-1PS) in respect to S and P.

S is symmetric square matrix.
P is a rectangular matrix

Could you help me?
Thank you very much

All the best

GoodSpirit

 

[GoodSpirit]

Hello everybody,

Perhaps I should explain a little bit.

The aim is to minimize an error metric and preferentially drive it to zero.
This should be done as function of S and P, as function of their rank and dimensions in particular.
By the way, the matrix A is symmetric too.

Many thanks

 

[GoodSpirit]

Hello,

Trying to update the equation presentation.

F(S,P)=tr(S-S P^T(A+PSP^T)^-1 PS)

A is positive definite

I've using matrix derivatives

What do you think?

All the best

GoodSpirit

 

[GoodSpirit]

LateX didn't work here

How to present an equation here?

Thank you

Good Spirit