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Open Access

Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

Journal of Inequalities and Applications20102010:939537

https://doi.org/10.1155/2010/939537

Received: 29 October 2009

Accepted: 14 March 2010

Published: 16 March 2010

Abstract

We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weir-type dual problems for our nonsmooth multiobjective problems and establish duality theorems for (weak) Pareto-optimal solutions under generalized convexity assumptions and regularity conditions.

Keywords

Optimality ConditionProgramming ProblemRegularity ConditionDual ProblemLipschitz Function

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Authors’ Affiliations

(1)
Division of Mathematical Sciences, Pukyong National University, Busan, South Korea

Copyright

© D. S. Kim and H. J. Lee. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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