Transformation of a non-convex constraint

Hello, everyone.

I have a non-convex constraint |\mathbf F|==\mathbf 1_{S\times S}, where \mathbf F is a S\times S complex variable matrix. It’s a unit-modulus constraint.

But actually I don’t need the constraint |\mathbf F|==1. I need to treat \mathbf X=\mathbf F\mathbf Q\mathbf F^H as a new variable, where \mathbf Q is a real symmetric matrix of size S\times S.

Do you have any suggestions on describing \mathbf F\mathbf Q\mathbf F^H as a new constraint by using the values of \mathbf Q and |\mathbf F|==1?

Thank you in advance.

As you say, it is a non-convex constraint. hence it would appear CVX is not the right tool for the problem.

Hi, Mark. You are right. Thank you for your response.