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Polynomial Primal-Dual Affine Scaling Algorithms in Semidefinite Programming

Author

Listed:
  • E. de Klerk

    (Delft University of Technology)

  • C. Roos

    (Delft University of Technology)

  • T. Terlaky

    (Delft University of Technology)

Abstract

Two primal-dual affine scaling algorithms for linear programming are extended to semidefinite programming. The algorithms do not require (nearly) centered starting solutions, and can be initiated with any primal-dual feasible solution. The first algorithm is the Dikin-type affine scaling method of Jansen et al. (1993b) and the second the classical affine scaling method of Monteiro et al. (1990). The extension of the former has a worst-case complexity bound of O(τ0nL) iterations, where τ0 is a measure of centrality of the the starting solution, and the latter a bound of O(τ0nL2) iterations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:2:y:1998:i:1:d:10.1023_a:1009791827917
    DOI: 10.1023/A:1009791827917
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    References listed on IDEAS

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    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. Renato D. C. Monteiro & Ilan Adler & Mauricio G. C. Resende, 1990. "A Polynomial-Time Primal-Dual Affine Scaling Algorithm for Linear and Convex Quadratic Programming and Its Power Series Extension," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 191-214, May.
    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.
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    Cited by:

    1. Ali Mohammad-Nezhad & Tamás Terlaky, 2017. "A polynomial primal-dual affine scaling algorithm for symmetric conic optimization," Computational Optimization and Applications, Springer, vol. 66(3), pages 577-600, April.

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