Extended Formulations in Combinatorial Optimization

TL;DR

This paper introduces the concept of extended formulations in combinatorial optimization, discussing recent advances in construction techniques and size lower bounds for representing complex polytopes efficiently.

Contribution

It provides an overview of recent developments in extended formulations, including new tools for their construction and bounds on their sizes.

Findings

Recent methods for constructing extended formulations

Lower bounds on the size of extended formulations

Enhanced understanding of polytope representations

Abstract

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the newsletter Optima of the Mathematical Optimization Society), we provide a brief introduction to this topic and sketch some of the recent developments with respect to both tools for constructing such extended formulations as well as lower bounds on their sizes.