Extended Formulations in Combinatorial Optimization

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.