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.

14 pages, 1 figure; Optima 85, 2011

Cited by in corpus (10)

• A special role of Boolean quadratic polytopes among other combinatorial polytopes
• Computing approximate PSD factorizations
• Positive Semidefinite Matrix Factorization: A Connection with Phase Retrieval and Affine Rank Minimization
• Extension complexity of stable set polytopes of bipartite graphs
• Online Learning of Combinatorial Objects via Extended Formulation
• Online Dynamic Programming
• An algebraic approach to symmetric extended formulations
• Extension Complexity of the Correlation Polytope
• Complexity of LP in Terms of the Face Lattice
• Balas formulation for the union of polytopes is optimal