Abstract and Applied Analysis
Volume 2013 (2013), Article ID 678154, 6 pages
http://dx.doi.org/10.1155/2013/678154
Research Article

Positive Definiteness of High-Order Subdifferential and High-Order Optimality Conditions in Vector Optimization Problems

He Qinghai1 and Zhang Binbin2

1Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
2School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, China

Received 15 October 2012; Accepted 26 December 2012

Academic Editor: Gue Lee

Copyright © 2013 He Qinghai and Zhang Binbin. 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 obtain a new Taylor's formula in terms of the order subdifferential of a function from to . As its applications in optimization problems, we build order sufficient optimality conditions of this kind of functions and order necessary conditions for strongly -quasiconvex functions.