cambrassk3

2022-07-03

I am trying to find the maximum of a hermitian positive definite quadratic form $xQ{x}^{H}$ (where $Q={Q}^{H}$ and all eigenvalues of $Q$ are non-negative) over the complex unit cube $|{x}_{i}|\le 1$, $i=1,\dots ,n$ where $x=\left({x}_{1},{x}_{2},\dots ,{x}_{n}\right)\in {\mathbb{C}}^{n}$.

This is the problem of minimizing a concave function over a convex domain. I have read that this problem is NP-hard but there exist some bounds on the optimum. What global optimization technique would your recommend to tackle this problem numerically? Since I am new to the field of optimization, I would appreciate every answer, thanks!

1s1zubv

Expert