Thumbnail Image
Item

Cuts and semidefinite liftings for the complex cut polytope

Sinjorgo,Lennart
; 
Sotirov,Renata
; 
Anjos,M.F.
Abstract
We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices xx H, where the elements of x∈C n are mth unit roots. These polytopes have applications in 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 polytope. We generalize valid cuts for this polytope to cuts for any complex cut polytope with finite m>2 and provide a framework to compare them. Further, we consider a second semidefinite lifting of the complex cut polytope for m=∞. This lifting is proven to be equivalent to other complex Lasserre-type liftings of the same order proposed in the literature, while being of smaller size. Our theoretical findings are supported by numerical experiments on various optimization problems.
Description
Publisher Copyright: © The Author(s) 2024.
Date
2024-10
Journal Title
Journal ISSN
Volume Title
Publisher
Collections
Tilburg University Research Output Collection
Show all metadata
Files
Thumbnail Image
2402.04731v3.pdf
Adobe PDF, 553.2 KB
Research Projects
Organizational Units
Journal Issue
Keywords
Complex semidefinite programming, Complex cut polytope, Polyhedral combinatorics, MIMO, Angular synchronization
Citation
Sinjorgo, L, Sotirov, R & Anjos, M F 2024, 'Cuts and semidefinite liftings for the complex cut polytope', Mathematical Programming. https://doi.org/10.1007/s10107-024-02147-3
URI
https://hdl.handle.net/20.500.14602/81763
Embedded videos