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

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...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.555-575-760
Main Authors: Pan, Shaohua, Bi, Shujun, Chen, Jein-Shan
Format: Article
Language:English
Subjects:
Jacobians
Mathematical optimization
Mathematical research
Nonlinear theories
Nonlinearity
Optimization
Programming
Regularity
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/602735