Trace minimization problem in MATLAB

Question

objective function: $\min_{X} F(X)$

constraint : $\operatorname{trace}(CXDX^H)\ge\alpha$

where A&C&Dis a matrix of $N\times N$ and X is matrix of $N\times N$ and F(X)=trace$(AX^HX)$

how this problem is solved in matlab?

Answer 1

You can vectorize all calculations and feed it into MATLAB's solver.

It won't give you the optimal solution only Local Minima as this is not a convex optimization problem.