## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 602735, 21 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511766

Digital Object Identifier
doi:10.1155/2013/602735

Mathematical Reviews number (MathSciNet)
MR3035226

Zentralblatt MATH identifier
1272.90047

#### Citation

Pan, Shaohua; Bi, Shujun; Chen, Jein-Shan. Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming. Abstr. Appl. Anal. 2013 (2013), Article ID 602735, 21 pages. doi:10.1155/2013/602735. https://projecteuclid.org/euclid.aaa/1393511766

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