Integer Programming

Abstract

A face F is said to be a facet of P if dim(F ) = dim(P )− 1. All facets are necessary (and sufficient) to describe a polyhedron. Facets do not have a unique description. But... Every full-dimensional polyhedron P has a unique (up to scalar multiplication) representation that consists of one inequality representing each facet of P . If dim(P ) = n− k with k > 0, then P is described by a maximal set of linearly independent rows of (A, b), as well as one inequality representing each facet of P .