How to write this objective function in CVX, see figure below. Thank you very much.
I will presume
w >= 0. Of course, if no constraints are added, H = matrix of zeros will be optimal with optimal objective value = 0.
cvx_begin variable H(n,n) V = sqrt(diag(w))*H'*X; minimize(vec(V)'*vec(V)) % place constraints here cvx_end
I believe that is convex for
C = ones(n)., i.e., for
However, I believe it is not convex for general elementwise nonnegative
C. For instance, let
C=[1 2;1 1]. Then the Hessian with respect to the 4 elements of
sum(vec(C.*(H*H'))) has two eigenvalues equal to 5 and two eigenvalues equal to -1, and hence is indefinite, so
sum(vec(C.*(H*H'))) is not convex.
You are right. Thanks.