# DCP error for sqrt of real positive diagonal matrix?

I have a minimization problem involving a nonlinear convex objective with respect to two matrix variables and subject to nonlinear (probably convex) constraints. I am able to formulate this in CVXOPT link text for real \mathbf{H} \in \mathcal{R}^{m\times n}, m\lt n and \mathbf{W} \in \mathcal{R}^{n\times m}.
However, I am not able to write this for neither real nor complex \mathbf{H} and \mathbf{W} in CVX and I get dcp error Invalid constraint: {complex affine} == {concave} for the second constraint. Can you please help me with this. Here comes the matlab code

cvx_begin
variable W(i,j) ;
variable P(j,j) hermitian diagonal;

minimize (sum(norms(W,2,2)))

subject to

norm(W,'fro')<=a
H*W==P.^0.5;
log_det(I+P)>=b

cvx_end


The optimization variable P is real positive diagonal matrix so the square root is valid. a and b are positive scalers.

The list of functions that CVX supports is here. Alas, sqrtm is not among them, although trace_sqrtm. Furthermore, the use of a nonlinear function in an equality constraint, even a convex one, almost always results in a non-convex problem. Nonlinear equality constraints are specifically disallowed by the DCP ruleset. Your problem simply is not compatible with CVX.