Similarity Transformations between Minimal Representations of Convex PolyhedralSets

摘要

A system of linear inhomogeneous inequalities determines a convex polyhedral setof feasible solutions. It is investigated under which conditions convex polyhedral sets can be represented also by a system that contains equalities as well as inequalities. Different representations of the same convex polyhedral set are related by elementary transformations. Necessary and sufficient conditions are derived for representations to contain the minimum number of equations necessary to describe a convex polyhedral set. Moreover, it is shown that minimal representations are related by so called similarity transformations.