Cuts and semidefinite liftings for the complex cut polytope

\(\) We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices \(xx^{\mathrm{H}}\), where the elements of \(x \in \mathbb{C}^n\) are \(m\)th unit roots. These polytopes have applications in \({\text{MAX-3-CUT}}\), digital communication technology, angular synchronization and more generally, complex quadratic programming. For \({m=2}\), the complex cut polytope corresponds to the well-known cut … Read more

A more efficient reformulation of complex SDP as real SDP

This note proposes a novel reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and derive some further reductions by exploiting structure of the complex SDP relaxations. Various numerical examples demonstrate that our new reformulation … Read more