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
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. By the way, the matrix A is symmetric too.