I have a problem in the following form:
$\underset{\mathbf{x}}{\text{min}} \mathbf{||Ax - b||^2_2}$
s.t $|[\mathbf{x}]_n| = 1; \forall n$
$\mathbf{A}$ is a complex $M \times N$ matrix and $\mathbf{x}$ and $\mathbf{b}$ is a $N \times 1$ vector. The problem is non-convex due to the constraint which says that each element of the complex vector $\mathbf{x}$ has unit modulus, i.e, a complex unit circle.
Hence, its difficult to find any closed form solution for the above problem. Can anyone kindly suggest any feasible optimization technique to solve the above problem.