Semidefinite Programming in cvx


I am doing SDP using cvx, as per the concept, min (x’Cx) === min trace(CX), X =x.x’

With linear constraints, this can be easily solved in cvx.

What if, my x is something like, x = f(y)exp(j*f(y)), where f(y) is some function.

Is the optimization problem convex? if not, or transformable to convex (for instance by Schur Complement), then CVX can;t be used to enter or solve it.

In CVX, any matrix being constrained to be semidefinite must be an affine (linear) function of the underlying optimization variables. Nonlinear SDPs are non-convex, and can’t be entered into CVX.