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Facial reduction for a cone-convex programming problem

Published online by Cambridge University Press:  09 April 2009

Jon M. Borwein  and
Henry Wolkowicz
Jon M. Borwein
Affiliation:
Department of Mathematics, Dalhousie University, Halifax, Canada
Henry Wolkowicz
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Canada
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Abstract

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In this paper we study the abstract convex program

where S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S (on Ω). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.

Keywords

Convexityabstract programmingfacial reductionexposed face

MSC classification

Secondary: 90C25: Convex programming
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 369 - 380
Copyright
Copyright © Australian Mathematical Society 1981

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