I am solving a convex program that is exactly the same as the one presented at this link. Namely, let A be a symmetric positive semidefinite matrix. I want to minimize H vec(A)  Y where vec(A) is the vectorized version of A and Y is a column vector.
I am experiencing 2 problems:

In my situation, I know the true value for A (and it satisfies the symmetric positive semidefinite constraint). When I plug this A into the objective function, I get a lower objective value than what is returned by CVX.

the optimal value by cvx, namely, cvx_optval is not exactly the same as what I would get by computing norm(H*A(:)Y) in matlab. cvx_optval is 2.5175e10 while Matlab provides me with 1.3138e10. Any insights on the issue?