convex optimization with non-linear constraint

Dear colleague

we have an optimization problem which has a convex objective with non-linear constraint. Looks like this, where C, A, W0 are known matrix, Z (matrix) and X (vector) are parameters to be solved.

    min_Z (C * Z - W0) 
    s.t. A .* (X * X') = Z;

unfortunately, the constraint here is non-linear. we can not optimize it using some convex optimization problem like, augmented Lagrangian method (attached code trying to solve the problem using augmented lagrangian, but the optimization did not converge at all). Can anybody give me some clue on how can I solve this problem? Thanks in advance.

Genzhi

[Matt J]

Your objective function looks matrix-valued, rather than scalar valued.