EUROPT 2024
Abstract Submission

246. Semidefinite liftings for the complex cut polytope

Invited abstract in session WC-2: Conic and Semidefinite Optimization, stream Conic optimization: theory, algorithms and applications.

Wednesday, 10:05 - 11:20
Room: M:O

Authors (first author is the speaker)

1. Miguel Anjos
School of Mathematics, University of Edinburgh
2. Lennart Sinjorgo
Tilburg University
3. Renata Sotirov
Tilburg University

Abstract

We consider the complex cut polytope: the convex hull of Hermitian rank-one matrices xx*, where the elements of the n-dimensional vector x are complex m-th unit roots. These polytopes find applications in MAX-3-CUT, digital communication, and more generally, complex quadratic programming. For m = 2, the complex cut polytope corresponds to the well-known real cut polytope. We provide an exact description of the complex cut polytope for m = n = 3 and investigate second order semidefinite liftings of the complex cut polytope. For such second order liftings, we show a method for reducing the size of the matrix, without weakening the approximation. We support our theoretical findings with numerical experiments.

Keywords

Status: accepted


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