Matrix trace minimization and zeros

by GoodSpirit
Tags: matrix, minimization, trace, zeros
 P: 19 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
 P: 19 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
 P: 19 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
P: 19

Matrix trace minimization and zeros

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Good Spirit

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