Trigonometric approximation of the Max-Cut Polytope is star-like

TL;DR

This paper proves Hirschfeld's conjecture that the trigonometric approximation of the Max-Cut polytope is star-like, enhancing understanding of its geometric structure and potential optimization approaches.

Contribution

The paper provides a proof confirming that the trigonometric approximation of the Max-Cut polytope is star-like, a conjecture previously unproven.

Findings

Confirmed the star-like nature of the trigonometric approximation

Enhanced understanding of the geometric structure of the Max-Cut polytope

Potential implications for optimization algorithms

Abstract

The Max-Cut polytope appears in the formulation of many difficult combinatorial optimization problems. These problems can also be formulated as optimization problems over the so-called trigonometric approximation which possesses an algorithmically accessible description but is not convex. Hirschfeld conjectured that this trigonometric approximation is star-like. In this article, we provide a proof of this conjecture.