Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 172059, 13 pages
Research Article

Optimality Conditions in Nondifferentiable G-Invex Multiobjective Programming

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

Received 29 October 2009; Revised 10 March 2010; Accepted 14 March 2010

Academic Editor: Jong Kyu Kim

Copyright © 2010 Ho Jung Kim et al. 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 consider a class of nondifferentiable multiobjective programs with inequality and equality constraints in which each component of the objective function contains a term involving the support function of a compact convex set. We introduce G-Karush-Kuhn-Tucker conditions and G-Fritz John conditions for our nondifferentiable multiobjective programs. By using suitable G-invex functions, we establish G-Karush-Kuhn-Tucker necessary and sufficient optimality conditions, and G-Fritz John necessary and sufficient optimality conditions of our nondifferentiable multiobjective programs. Our optimality conditions generalize and improve the results in Antczak (2009) to the nondifferentiable case.