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Characterization of optimality for the abstract convex program with finite dimensional range

Published online by Cambridge University Press:  09 April 2009

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

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This paper presents characterizations of optimality for the abstract convex program

when 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-convex (on Ω). These characterizations, which include a Lagrange multiplier theorem and do not presume any a priori constraint qualification, subsume those presently in the literature.

Keywords

convexityabstract programmingLagrange multipliersSlater's conditionsubgradientsduality principlesfacial reductionsymmetric matricescone of positive semi-definite matrices

MSC classification

Secondary: 90C25: Convex programming
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 4 , April 1981 , pp. 390 - 411
Copyright
Copyright © Australian Mathematical Society 1981

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