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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.

Suggested Citation

  • Shaohua Pan & Shujun Bi & Jein-Shan Chen, 2013. "Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-21, March.
    • Handle: RePEc:hin:jnlaaa:602735
    DOI: 10.1155/2013/602735
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