Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 620928, 17 pages
doi:10.1155/2010/620928
Research Article

Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems

Ying Gao,1 Xinmin Yang,1 and Heung Wing Joseph Lee2

1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received 18 July 2010; Accepted 25 October 2010

Academic Editor: Mohamed El-Gebeily

Copyright © 2010 Ying Gao 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 study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone, 𝜀 -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.