Abstract
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.
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