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Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization

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An Erratum to this article was published on 30 March 2017

Abstract

In this paper, an improved complexity analysis of full Nesterov–Todd step feasible interior-point method for symmetric optimization is considered. Specifically, we establish a sharper quadratic convergence result using several new results from Euclidean Jordan algebras, which leads to a wider quadratic convergence neighbourhood of the central path for the iterates in the algorithm. Furthermore, we derive the currently best known iteration bound for full Nesterov–Todd step feasible interior-point method.

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Acknowledgments

The first author would like to thank Dr. Guoyong Gu (Nanjing University) for his insightful comments and suggestions on an earlier draft of this article. The authors would like to thank the handling editor and the anonymous referees for their useful comments and suggestions, which helped to improve the presentation of this paper. This work was supported by National Natural Science Foundation of China (Nos. 11471211, 11171018) and Shanghai Natural Science Fund Project (No. 14ZR1418900).

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Authors and Affiliations

  1. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201620, People’s Republic of China

    G. Q. Wang

  2. Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    L. C. Kong

  3. Department of Mathematics and Statistics, Loyola University Maryland, Baltimore, MD, 21210, USA

    J. Y. Tao

  4. Department of Industrial Engineering, Yasar University, Izmir, Turkey

    G. Lesaja

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  1. G. Q. Wang
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  2. L. C. Kong
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  3. J. Y. Tao
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Correspondence to G. Q. Wang.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s10957-016-1015-x.

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Wang, G.Q., Kong, L.C., Tao, J.Y. et al. Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization. J Optim Theory Appl 166, 588–604 (2015). https://doi.org/10.1007/s10957-014-0696-2

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  • DOI: https://doi.org/10.1007/s10957-014-0696-2

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