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Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

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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.

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Correspondence to DoSang Kim.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Kim, D., Lee, H. Optimality Conditions and Duality in Nonsmooth Multiobjective Programs. J Inequal Appl 2010, 939537 (2010) doi:10.1155/2010/939537

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Keywords

  • Optimality Condition
  • Programming Problem
  • Regularity Condition
  • Dual Problem
  • Lipschitz Function