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Duality theorems for convex programming without constraint qualification

Published online by Cambridge University Press:  09 April 2009

P. Kanniappan
P. Kanniappan
Affiliation:
School of Mathematics Madurai Kamaraj UniversityMadurai-625 021 Tamil Nadu, India Department of Mathematics Gandhigram Rural InstituteGandhigram-624 302 Tamil Nadu, India
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Abstract

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Invoking a recent characterization of Optimality for a convex programming problem with finite dimensional range without any constraint qualification given by Borwein and Wolkowicz, we establish duality theorems. These duality theorems subsume numerous earlier duality results with constraint qualifications. We apply our duality theorems in the case of the objective function being the sum of a positively homogeneous, lower-semi-continuous, convex function and a subdifferentiable convex function. We also study specific problems of the above type in this setting.

MSC classification

Secondary: 90C25: Convex programming 90C30: Nonlinear programming 90C48: Programming in abstract spaces

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 2 , April 1984 , pp. 253 - 266
Copyright
Copyright © Australian Mathematical Society 1984

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