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Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming

Author

Listed:
  • Arjan B. Berkelaar

    (Erasmus University Rotterdam)

  • Jos F. Sturm

    (Erasmus University Rotterdam)

  • Shuzhong Zhang

    (Erasmus University Rotterdam)

Abstract

In this paper we generalize the primal--dual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming.We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefiniteprogramming, resulting in a new algorithm. Compared to other primal--dual affine scaling algorithms for semidefiniteprogramming (see, De Klerk, Roos and Terlaky), our algorithm enjoys the lowest computationalcomplexity.

Suggested Citation

  • Arjan B. Berkelaar & Jos F. Sturm & Shuzhong Zhang, 1997. "Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming," Tinbergen Institute Discussion Papers 97-025/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19970025
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    References listed on IDEAS

    as
    1. Sturm, J.F. & Zhang, S., 1995. "Symmetric primal-dual path following algorithms for semidefinite programming," Econometric Institute Research Papers EI 9554-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. NESTEROV ., Yurii E. & TODD , Michael J, 1994. "Self-Scaled Cones and Interior-Point Methods in Nonlinear Programming," LIDAM Discussion Papers CORE 1994062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Sturm, J.F. & Zhang, S., 1996. "On Weighted Centers for Semidefinite Programming," Econometric Institute Research Papers EI 9636-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. NESTEROV , Yurii & TODD , Michael, 1995. "Primal-Dual Interior-Point Methods for Self-Scaled Cones," LIDAM Discussion Papers CORE 1995044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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