Minimum principle sufficiency
type: Item
instance of: scholarly article
title: Minimum principle sufficiency
zbMATH Open document ID: 0760.90076
DOI: 10.1007/BF01581071
author: Michael C. Ferris
author: O. L. Mangasarian
published in: Mathematical Programming. Series A. Series B
publication date: 1993-01-16T00:00:00Z
review text: The authors study the determination of a solution of a convex program by minimizing over the feasible region a linearized form of the objective function at any of its solution points (Minimum Principle Sufficiency, shortly MPS). Thus, for the case of a monotone linear complementarity problem the MPS property is equivalent to the existence of a nondegenerate solution to the problem. For the case of a convex quadratic program, the MPS property is equivalent to the span of the Hessian of the objective function being contained in the normal cone to the feasible region at any solution point, plus the cone generated by the gradient of the objective function at any solution point. This in turn is equivalent to the quadratic program having a weak sharp minimum. An important application of the MPS property is that minimizing on the feasible region a linearization of the objective function at a point in a neighborhood of a solution point gives an exact solution of the convex program.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 92712
zbMATH Keywords: minimum principle
zbMATH Keywords: monotone linear complementarity
reviewed by: Stefan Mititelu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 92712