Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 857520, 13 pages
doi:10.1155/2011/857520
Research Article

Second-Order Contingent Derivative of the Perturbation Map in Multiobjective Optimization

Q. L. Wang1 and S. J. Li2

1College of Sciences, Chongqing Jiaotong University, Chongqing 400074, China
2College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China

Received 14 October 2010; Accepted 24 January 2011

Academic Editor: Jerzy Jezierski

Copyright © 2011 Q. L. Wang and S. J. Li. 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

Some relationships between the second-order contingent derivative of a set-valued map and its profile map are obtained. By virtue of the second-order contingent derivatives of set-valued maps, some results concerning sensitivity analysis are obtained in multiobjective optimization. Several examples are provided to show the results obtained.