International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 2, Article ID 30459, 11 pages
doi:10.1155/IJMMS/2006/30459

Duality without constraint qualification in nonsmooth optimization

Abstract

We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualification. Then we formulate the dual problem corresponding to the primal problem, and some duality results are obtained without a constraint qualification.