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Improved Complexity Analysis of Full Nesterov–Todd Step Interior-Point Methods for Semidefinite Optimization

Author

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  • G. Q. Wang

    (Shanghai University of Engineering Science)

  • Y. Q. Bai

    (Shanghai University)

  • X. Y. Gao

    (Heilongjiang University)

  • D. Z. Wang

    (Shanghai University of Engineering Science)

Abstract

In this paper, we present an improved convergence analysis of full Nesterov–Todd step feasible interior-point method for semidefinite optimization, and extend it to the infeasible case. This improvement due to a sharper quadratic convergence result, which generalizes a known result in linear optimization and leads to a slightly wider neighborhood for the iterates in the feasible algorithm and for the feasibility steps in the infeasible algorithm. For both versions of the full Nesterov–Todd step interior-point methods, we derive the same order of the iteration bounds as the ones obtained in linear optimization case.

Suggested Citation

  • G. Q. Wang & Y. Q. Bai & X. Y. Gao & D. Z. Wang, 2015. "Improved Complexity Analysis of Full Nesterov–Todd Step Interior-Point Methods for Semidefinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 242-262, April.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0619-2
    DOI: 10.1007/s10957-014-0619-2
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    References listed on IDEAS

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    1. 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.
    2. G. Gu & H. Mansouri & M. Zangiabadi & Y. Q. Bai & C. Roos, 2010. "Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 271-288, May.
    3. 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.
    4. 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.
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    Cited by:

    1. Chee-Khian Sim, 2019. "Interior point method on semi-definite linear complementarity problems using the Nesterov–Todd (NT) search direction: polynomial complexity and local convergence," Computational Optimization and Applications, Springer, vol. 74(2), pages 583-621, November.

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