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New Complexity Analysis of the Primal–Dual Method for Semidefinite Optimization Based on the Nesterov–Todd Direction

Author

Listed:
  • J. PENG

    (Delft University of Technology)

  • C. ROOS

    (Delft University of Technology)

  • T. TERLAKY

    (McMaster University)

Abstract

Interior-point methods for semidefinite optimization have been studied intensively in recent times, due to their polynomial complexity and practical efficiency. In this paper, first we present some technical results about symmetric matrices. Then, we apply these results to give a unified analysis for both large update and small update interior-point methods for SDP based on the Nesterov–Todd (NT) direction.

Suggested Citation

  • J. Peng & C. Roos & T. Terlaky, 2001. "New Complexity Analysis of the Primal–Dual Method for Semidefinite Optimization Based on the Nesterov–Todd Direction," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 327-343, May.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:2:d:10.1023_a:1017514422146
    DOI: 10.1023/A:1017514422146
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    References listed on IDEAS

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    1. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
    2. Andersen, E.D. & Gondzio, J. & Meszaros, C. & Xu, X., 1996. "Implementation of Interior Point Methods for Large Scale Linear Programming," Papers 96.3, Ecole des Hautes Etudes Commerciales, Universite de Geneve-.
    3. Kurt M. Anstreicher & Jun Ji & Florian A. Potra & Yinyu Ye, 1999. "Probabilistic Analysis of an Infeasible-Interior-Point Algorithm for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 176-192, February.
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