Similarity transformations between minimal representations of convex polyhedral sets

Report (1993)

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Optimization Inequalities Set theory Representations Matrices (mathematics) Convexity Cones Polyhedrons Similarity theorem Transformations (mathematics
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Published Date

15-08-1993

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NLR Technical Publication TP 93393 U

Abstract

A system of linear inhomogeneous inequalities determines a convex polyhedral set of 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.

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