Abstract and Applied Analysis
Volume 2012 (2012), Article ID 909520, 11 pages
http://dx.doi.org/10.1155/2012/909520
Research Article

Necessary Conditions for Weak Sharp Minima in Cone-Constrained Optimization Problems

W. Y. Zhang,1 S. Xu,2 and S. J. Li3

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China
2Rear Services Office, Chongqing Police College, Chongqing 401331, China
3College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received 11 January 2012; Accepted 29 January 2012

Academic Editor: Bevan Thompson

Copyright © 2012 W. Y. Zhang 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 weak sharp minima for optimization problems with cone constraints. Some necessary conditions for weak sharp minima of higher order are established by means of upper Studniarski or Dini directional derivatives. In particular, when the objective and constrained functions are strict derivative, a necessary condition is obtained by a normal cone.