Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 939537, 12 pages
Research Article

Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

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

Received 29 October 2009; Accepted 14 March 2010

Academic Editor: Jong Kyu Kim

Copyright © 2010 Do Sang Kim and Hyo Jung Lee. 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.


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.