Convex hull restriction over complex variable, is possible?

Nonconvex
1

Hi, new in CVX

It is possible to formulate this problem in CVX, I have tried without success.

A is a 3x3 real (constant) matrix, v is a 3x1 COMPLEX valued vector.

Minimize x’*A’Ax-(abs(x’Ax))^2
s.t. x’*x==1

Any help?

2

This model is not convex, so no.