I have a function, F, to minimize. Let's assume:
$F(X,Y,Z) = G(A-YX)^2 - H(B-ZYY')^2 $
Where $X, Y, Z$ are my unknown variables in a matrix shape, and the matrices $A, B$ are the given ones.
I know all the subjects about necessity and sufficient conditions --taking derivatives, Hermitian matrix and calculating its eigenvalues and etc. But my question is: are the ordinary methods applicable to this equation?
I will be thankful if some hint me how to solve this equation by using the above-mentioned methods.
Besides that, I know that we always try to convert a set of linear equations (some cases nonlinear) into a matrix notation form, but what should we do if we have equations which its parameters are matrices?
Sincerely yours,