Abstract and Applied Analysis
Volume 2013 (2013), Article ID 602735, 21 pages
http://dx.doi.org/10.1155/2013/602735
Research Article

Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming

Shaohua Pan,1 Shujun Bi,1 and Jein-Shan Chen2

1Department of Mathematics, South China University of Technology, Guangzhou 510641, China
2Mathematics Division, National Center for Theoretical Sciences, Taipei 11677, Taiwan

Received 2 June 2012; Accepted 9 December 2012

Academic Editor: Narcisa C. Apreutesei

Copyright © 2013 Shaohua Pan 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

This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP), specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB) nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.