A short proof for the polyhedrality of the Chv\'atal-Gomory closure of a compact convex set

TL;DR

This paper provides a concise and accessible proof demonstrating that the Chvatal-Gomory closure of any compact convex set is a polytope, resolving a long-standing open problem in the field.

Contribution

It offers a new, simplified proof confirming the polyhedrality of the Chvatal-Gomory closure for compact convex sets, building on recent solutions to Schrijver's open problem.

Findings

Chvatal-Gomory closure of compact convex sets is a polytope

Simplified proof approach enhances understanding

Addresses a long-standing open problem in polyhedral theory

Abstract

Recently Schrijver's open problem, whether the Chv\'atal--Gomory closure of an irrational polytope is polyhedral was answered independently in the affirmative by Dadush, Dey, and Vielma (even for arbitrarily compact convex set) as well as by Dunkel and Schulz. We present a very short, easily accesible proof that the Chv\'atal--Gomory closure of a compact convex set is a polytope.