A Constructive Proof of the Representation Theorem for Polyhedral Sets Based on Fundamental Definitions
Hanif D. Sherali · American Journal of Mathematical and Management Sciences · 1987
SYNOPTIC ABSTRACTThis paper provides a constructive, geometrically motivated proof for the well known and important Representation (or Resolution) Theorem for polyhedral sets. One principal value of this proof is pedagogical: it provides geometric insights, and is based purely on the definitions of extreme points and directions and simple associated geometric concepts. However, the proof also suggests a polynomial time algorithm for actually constructing a representation of a given point belonging to a polyhedral set in terms of the extreme points and extreme directions of this polyhedron. Details of this algorithm along with a numerical example and discussions of some related issues are also presented.