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Duality theorems and an optimality condition for non-differentiable convex programming

Published online by Cambridge University Press:  09 April 2009

P. Kanniappan  and
Sundaram M. A. Sastry
P. Kanniappan
Affiliation:
School of Mathematics, Madurai Kamaraj University, Madurai-625 021, Tamil Nadu, India
Sundaram M. A. Sastry
Affiliation:
School of Mathematics, Madurai Kamaraj University, Madurai-625 021, Tamil Nadu, India
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Abstract

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Necessary and sufficient optimality conditions of Kuhn-Tucker type for a convex programming problem with subdifferentiable operator constraints have been obtained. A duality theorem of Wolfe's type has been derived. Assuming that the objective function is strictly convex, a converse duality theorem is obtained. The results are then applied to a programming problem in which the objective function is the sum of a positively homogeneous, lower-semi-continuous, convex function and a continuous convex function.

MSC classification

Secondary: 90C25: Convex programming 90C30: Nonlinear programming 90C48: Programming in abstract spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 3 , June 1982 , pp. 369 - 379
Copyright
Copyright © Australian Mathematical Society 1982

References

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