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Technical Note: Some Structural Properties of a Newton-Type Method for Semidefinite Programs

Author

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  • C. Kanzow

    (University of Würzburg)

  • C. Nagel

    (University of Würzburg)

Abstract

Using the minimum function or the Fischer-Burmeister function, we obtain two reformulations of a semidefinite program as a nonlinear system of equations. Applying a Newton-type method to such a reformulation leads to a linear system of equations which has to be solved at each iteration. We discuss some properties of this linear system and show that the corresponding coefficient matrix is symmetric positive definite for the minimum function approach and positive definite but unsymmetric for the Fischer-Burmeister formulation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:1:d:10.1023_b:jota.0000041737.19689.4c
    DOI: 10.1023/B:JOTA.0000041737.19689.4c
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    References listed on IDEAS

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    1. Defeng Sun & Jie Sun, 2002. "Semismooth Matrix-Valued Functions," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 150-169, February.
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    Cited by:

    1. 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.

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