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A trust region method for solving semidefinite programs

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Listed:
  • Aiqun Huang
  • Chengxian Xu

Abstract

When using interior point methods for solving semidefinite programs (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, we propose a trust region algorithm for solving SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Aiqun Huang & Chengxian Xu, 2013. "A trust region method for solving semidefinite programs," Computational Optimization and Applications, Springer, vol. 55(1), pages 49-71, May.
    • Handle: RePEc:spr:coopap:v:55:y:2013:i:1:p:49-71
    DOI: 10.1007/s10589-012-9514-7
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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.
    2. 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.
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