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  • Research Article
  • Open Access

Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

Journal of Inequalities and Applications20102010:939537

  • Received: 29 October 2009
  • Accepted: 14 March 2010
  • Published:


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.


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

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Authors’ Affiliations

Division of Mathematical Sciences, Pukyong National University, Busan, 608-737, South Korea


© 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.