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Equivalent Conditions for Jacobian Nonsingularity in Linear Symmetric Cone Programming

Author

Listed:
  • Lingchen Kong

    (Beijing Jiaotong University
    University of Waterloo)

  • Levent Tunçel

    (University of Waterloo)

  • Naihua Xiu

    (Beijing Jiaotong University)

Abstract

In this paper we consider the linear symmetric cone programming (SCP). At a Karush-Kuhn-Tucker (KKT) point of SCP, we present the important conditions equivalent to the nonsingularity of Clarke’s generalized Jacobian of the KKT nonsmooth system, such as primal and dual constraint nondegeneracy, the strong regularity, and the nonsingularity of the B-subdifferential of the KKT system. This affirmatively answers an open question by Chan and Sun (SIAM J. Optim. 19:370–396, 2008).

Suggested Citation

  • Lingchen Kong & Levent Tunçel & Naihua Xiu, 2011. "Equivalent Conditions for Jacobian Nonsingularity in Linear Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 364-389, February.
    • Handle: RePEc:spr:joptap:v:148:y:2011:i:2:d:10.1007_s10957-010-9758-2
    DOI: 10.1007/s10957-010-9758-2
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    References listed on IDEAS

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    4. Defeng Sun & Jie Sun, 2008. "Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 421-445, May.
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    Cited by:

    1. Bruno F. Lourenço & Ellen H. Fukuda & Masao Fukushima, 2018. "Optimality Conditions for Problems over Symmetric Cones and a Simple Augmented Lagrangian Method," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1233-1251, November.

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