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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, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:602735
    DOI: 10.1155/2013/602735
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    References listed on IDEAS

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    1. Jong-Shi Pang & Defeng Sun & Jie Sun, 2003. "Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 39-63, February.
    2. Yun Wang & Liwei Zhang, 2009. "Properties of equation reformulation of the Karush–Kuhn–Tucker condition for nonlinear second order cone optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 195-218, October.
    3. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    4. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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    Cited by:

    1. Xiaoni Chi & Zhongping Wan & Zijun Hao, 2013. "The Jacobian Consistency of a One‐Parametric Class of Smoothing Functions for SOCCP," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Kuo-Yang Wu & Sendren Sheng-Dong Xu & Tzong-Chen Wu, 2013. "Optimal Scheduling for Retrieval Jobs in Double‐Deep AS/RS by Evolutionary Algorithms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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