I am implementing an optimization problem using semi-definite problem. One of my constraints is of following form
$$trace(A*X)- (k * trace(A*X))+ (k * \sqrt{trace(B*X)})==0$$
where k is a constant, $A$ and $B$ are constant complex hermitian matrices and $X$ is $m*m$ complex, hermitian semi definite matrix optimization variable.
It can be seen that the last terms $\sqrt{trace(B*X)}$ is a problematic term. Since, I am writing my code using YALMIP, which is an external toolbox of MATLAB, sqrt on complex variable is not allowed in that toolbox. Is there any way to rewrite that particular term using some convex optimization tools so that I can implement it easily in YALMIP?