Table of Contents
ISRN Applied Mathematics
Volume 2014 (2014), Article ID 904640, 11 pages
http://dx.doi.org/10.1155/2014/904640
Research Article

Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

1Centre for Mathematical Sciences, Banasthali University, Rajasthan 304022, India
2Department of Applied Sciences and Humanities, ITM University, Gurgaon 122017, India
3Department of Mathematics, South Asian University, New Delhi 110021, India

Received 18 February 2014; Accepted 25 March 2014; Published 22 May 2014

Academic Editors: P.-y. Nie and S. Utyuzhnikov

Copyright © 2014 Pallavi Kharbanda 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.

Abstract

We consider a nonsmooth multiobjective programming problem where the functions involved are nondifferentiable. The class of univex functions is generalized to a far wider class of - -V-type I univex functions. Then, through various nontrivial examples, we illustrate that the class introduced is new and extends several known classes existing in the literature. Based upon these generalized functions, Karush-Kuhn-Tucker type sufficient optimality conditions are established. Further, we derive weak, strong, converse, and strict converse duality theorems for Mond-Weir type multiobjective dual program.