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A New Strategy in the Complexity Analysis of an Infeasible-Interior-Point Method for Symmetric Cone Programming

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  • Ximei Yang

    (Xidian University
    Henan Normal University)

  • Hongwei Liu

    (Xidian University)

  • Yinkui Zhang

    (Henan Normal University)

Abstract

In this paper, we give a new strategy in the complexity analysis of an infeasible-interior-point method for symmetric cone programming. Using the strategy, we improve the theoretical complexity bound of an infeasible-interior-point method. Convergence is shown for a commutative class of search directions, which includes the Nesterov–Todd direction and the $$xs$$ x s and $$sx$$ s x directions.

Suggested Citation

  • Ximei Yang & Hongwei Liu & Yinkui Zhang, 2015. "A New Strategy in the Complexity Analysis of an Infeasible-Interior-Point Method for Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 572-587, August.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:2:d:10.1007_s10957-014-0670-z
    DOI: 10.1007/s10957-014-0670-z
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    References listed on IDEAS

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    1. F. A. Potra & R. Sheng, 1998. "Superlinearly Convergent Infeasible-Interior-Point Algorithm for Degenerate LCP," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 249-269, May.
    2. 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.
    3. G. Q. Wang & Y. Q. Bai, 2012. "A New Full Nesterov–Todd Step Primal–Dual Path-Following Interior-Point Algorithm for Symmetric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 966-985, September.
    4. 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.
    5. Gu, G. & Zangiabadi, M. & Roos, C., 2011. "Full Nesterov-Todd step infeasible interior-point method for symmetric optimization," European Journal of Operational Research, Elsevier, vol. 214(3), pages 473-484, November.
    6. Hongwei Liu & Ximei Yang & Changhe Liu, 2013. "A New Wide Neighborhood Primal–Dual Infeasible-Interior-Point Method for Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 796-815, September.
    7. Changhe Liu & Hongwei Liu & Xinze Liu, 2012. "Polynomial Convergence of Second-Order Mehrotra-Type Predictor-Corrector Algorithms over Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 949-965, September.
    8. Jian Zhang & Kecun Zhang, 2011. "Polynomial complexity of an interior point algorithm with a second order corrector step for symmetric cone programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 75-90, February.
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    Cited by:

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    2. Héctor Ramírez & David Sossa, 2017. "On the Central Paths in Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 649-668, February.
    3. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Erdoğan, Fevzi, 2019. "Stochastic numerical approach for solving second order nonlinear singular functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.

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