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

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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.

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Acknowledgments

The authors would like to thank Professor Kok Lay Teo and the anonymous referees for their useful comments and suggestions, which helped to improve the presentation of this paper. This work was supported by Shanghai Natural Science Fund Project (14ZR1418900), National Natural Science Foundation of China (Nos. 11001169,11371242), China Postdoctoral Science Foundation funded project (Nos. 2012T50427, 20100480604) and Natural Science Foundation of Shanghai University of Engineering Science (No. 2014YYYF01).

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Authors and Affiliations

  1. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai , 201620, China

    G. Q. Wang

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Y. Q. Bai

  3. School of Mathematical Science, Heilongjiang University, Harbin, 150080, China

    X. Y. Gao

  4. Department of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    D. Z. Wang

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  1. G. Q. Wang
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  2. Y. Q. Bai
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  3. X. Y. Gao
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  4. D. Z. Wang
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Correspondence to G. Q. Wang.

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Communicated by Kok Lay Teo.

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Wang, G.Q., Bai, Y.Q., Gao, X.Y. et al. Improved Complexity Analysis of Full Nesterov–Todd Step Interior-Point Methods for Semidefinite Optimization. J Optim Theory Appl 165, 242–262 (2015). https://doi.org/10.1007/s10957-014-0619-2

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  • DOI: https://doi.org/10.1007/s10957-014-0619-2

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