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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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    1. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    2. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    3. Defeng Sun & Jie Sun, 2002. "Semismooth Matrix-Valued Functions," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 150-169, February.
    4. Stephen M. Robinson, 2003. "Constraint Nondegeneracy in Variational Analysis," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 201-232, May.
    5. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    6. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    7. 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.
    8. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
    9. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    10. M. L. Flegel & C. Kanzow, 2007. "Equivalence of Two Nondegeneracy Conditions for Semidefinite Programs," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 381-397, December.
    11. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
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