Extended formulations, nonnegative factorizations, and randomized communication protocols

• Published in: Mathematical programming Vol. 153; no. 1; pp. 75 - 94
• Main Authors: Faenza, Yuri, Fiorini, Samuel, Grappe, Roland, Tiwary, Hans Raj
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2015; Springer Nature B.V
• Subjects: Algorithms; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Communication; Complexity; Computation; Factorization; Full Length Paper; Geometry; Graphs; Logarithms; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical models; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Optimization; Optimization algorithms; Polyhedra; Polyhedrons; Polytopes; Protocol; Studies; Theorems; Theoretical; 52B05

An extended formulation of a polyhedron P is a linear description of a polyhedron Q together with a linear map π such that π ( Q ) = P . These objects are of fundamental importance in polyhedral combinatorics and optimization theory, and the subject of a number of studies. Yannakakis’ factorization...