International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 30459, 11 pages

Duality without constraint qualification in nonsmooth optimization

S. Nobakhtian

Department of Mathematics, University of Isfahan, Isfahan 81745-163, Iran

Received 7 May 2005; Revised 26 July 2005; Accepted 1 January 2006

Copyright © 2006 S. Nobakhtian. 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 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.