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

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  • Shaohua Pan
  • Shujun Bi
  • Jein-Shan Chen

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.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:602735
DOI: 10.1155/2013/602735
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