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Symmetric primal-dual path following algorithms for semidefinite programming

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  • Sturm, J.F.
  • Zhang, S.

Abstract

In this paper a symmetric primal-dual transformation for positive semidefinite programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear programming, existence of such a primal-dual transformation is a well known fact. Based on this symmetric primal-dual transformation we derive Newton search directions for primal-dual path-following algorithms for semidefinite programming. In particular, we generalize: (1) the short step path following algorithm, (2) the predictor-corrector algorithm and (3) the largest step algorithm to semidefinite programming. It is shown that these algorithms require at most [TeX: ${\\cal O}(\\sqrt{n}\\mid \\log \\epsilon \\mid ) $] main iterations for computing an [TeX: $\\epsilon $]-optimal solution.

Suggested Citation

  • 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.
    • Handle: RePEc:ems:eureir:1364
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    Citations

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    Cited by:

    1. E. de Klerk & C. Roos & T. Terlaky, 1998. "Polynomial Primal-Dual Affine Scaling Algorithms in Semidefinite Programming," Journal of Combinatorial Optimization, Springer, vol. 2(1), pages 51-69, March.
    2. 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.
    3. de Klerk, E. & Roos, C. & Terlaky, T., 1997. "Initialization in semidefinite programming via a self-dual, skew-symmetric embedding," Other publications TiSEM aa045849-1e10-4f84-96ca-4, Tilburg University, School of Economics and Management.
    4. F. A. Potra & R. Sheng, 1998. "Superlinear Convergence of Interior-Point Algorithms for Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 103-119, October.

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