Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming. (11th March 2013)

• Record Type: Journal Article
• Authors: Pan, Shaohua; Bi, Shujun; Chen, Jein-Shan
• Other Names: Apreutesei Narcisa C. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-03-11
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/602735
• Languages: English
• ISSNs: 1085-3375

Abstract

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.