Convex Optimization for Matlab

Question

I want to know how can i solve the following minimization problem with matlab:

A is a semi-positive definite matrix. (All eigenvalues are greater or iqual than 0) F=F(x_1,...,x_n,y_1,y_2) = (F_1,...,F_2n) is a linear function.

i want to find (x_1,...,x_n,y_1,y_2) so that:

F*A*F' is minimum. There are no restriction in the variables, but notice that there are substantially less than the vector length.

I am trying to minicime a statistical distance. I can't find on the web what functions to use.

Thanks in advance.

Answer 1

for unconstrained optimization in MATLAB you can use fminunc. To do so, you can define your cost function:

function z = costfun(x)
f = F*A*F';    % where F is a function of x=[x_1,...y_n]

then call fminunc to find the minimum. Vector x0 is provided as a starting point for searching.

[x,zval] = fminunc(@costfun,x0);