International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 30459, 11 pages
doi:10.1155/IJMMS/2006/30459
Duality without constraint qualification in nonsmooth optimization
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.
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.