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Equivalence of Two Nondegeneracy Conditions for Semidefinite Programs

Author

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  • M. L. Flegel

    (University of Würzburg)

  • C. Kanzow

    (University of Würzburg)

Abstract

Nondegeneracy assumptions are often needed in order to prove the local fast convergence of suitable algorithms as well as in the sensitivity analysis for semidefinite programs. One of the more standard nondegeneracy conditions is the geometric condition used by Alizadeh et al. (Math. Program. 77:111–128, 1997). On the other hand, Kanzow and Nagel (SIAM J. Optim. 15:654–672, 2005) recently introduced an algebraic condition that was used in order to prove, for the first time, the local quadratic convergence of a suitable algorithm for the solution of semidefinite programs without using the strict complementarity assumption. The aim of this paper is to show that these two nondegeneracy conditions are equivalent.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9270-5
    DOI: 10.1007/s10957-007-9270-5
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    References listed on IDEAS

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    1. E. A. Yıldırım, 2003. "An Interior-Point Perspective on Sensitivity Analysis in Semidefinite Programming," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 649-676, November.
    2. Defeng Sun & Jie Sun, 2002. "Semismooth Matrix-Valued Functions," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 150-169, February.
    3. C. Kanzow & C. Nagel, 2004. "Technical Note: Some Structural Properties of a Newton-Type Method for Semidefinite Programs," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 219-226, July.
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    Cited by:

    1. Houduo Qi, 2009. "Local Duality of Nonlinear Semidefinite Programming," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 124-141, February.
    2. 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.

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