Minimal representation of convex regions defined by analytic functions

Minimal representation of convex regions defined by analytic functions

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Article ID: iaor20012972
Country: United States
Volume: 246
Start Page Number: 100
End Page Number: 121
Publication Date: Jan 2000
Journal: Journal of Mathematical Analysis and Applications
Authors:
Abstract:

In this paper we are concerned with characterizing minimal representation of feasible regions defined by both linear and convex analytic constraints. We say that a representation is minimal if every other representation has either more analytic (nonlinear) constraints, or has the same number of analytic constraints and at least as many linear constraints. We prove necessary and sufficient conditions for the representation to be minimal. These are expressed in terms of the redundant constraints, pseudo-analytic constraints, and implicit equality constraints. In order to prove the minimal representation theorem, we present results on the facets of the convex regions defined by analytic constraints. Finally, we outline the steps of the procedure that could be used to determine a minimal representation.

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