A new characterization of the center of a polytope

Abstract

The main contribution of this work is the introduction of a new function which has the analytic center of a polytope as its maximizer. At the function's optimal point, it assumes a value equal to m, the total number of constraints used to define the polytope. For this reason we call it the m-function of the polytope. We also prove that given a p-dimensional face of a nondegenerate polytope the m-function for that polytope assumes the value m-(n-p) at the analytic center of the face. In particular the m-function assumes the value m at the analytic center of the polytope.16318520