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On the \(O(1/t)\) convergence rate of the LQP prediction–correction method

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Abstract

The logarithmic-quadratic proximal (abbreviated by LQP) prediction–correction method is attractive for structured monotone variational inequalities, and it ensures the global convergence under some suitable conditions. In this paper, we are interested in investigating the convergence rate of the LQP prediction–correction method. Motivated by the research work about the convergence rate or iteration complexity for various first-order algorithms in the literature, we provide a simple proof to show the \(O(1/t)\) convergence rate for the LQP prediction–correction method.

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Acknowledgments

The first author was supported by National Science and Technology Support Program (Grant No. 2011BAH24B06), Joint Fund of National Natural Science Foundation of China and Civil Aviation Administration of China (Grant No. U1233105) and Science Foundation of the Civil Aviation Flight University of China (Grant No. J2010-45). The second author was supported by National Natural Science Foundation of China (Grant No. 11001053) and Natural Science Foundation of Jiangsu Province, China (Grant No. BK2012662).

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Authors and Affiliations

  1. School of Computer Science, Civil Aviation Flight University of China, Guanghan, 618307, China

    Haiwen Xu

  2. School of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Haiwen Xu

  3. School of Economics and Management, Southeast University, Nanjing, 210096, China

    Min Li

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  1. Haiwen Xu
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  2. Min Li
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Correspondence to Min Li.

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Xu, H., Li, M. On the \(O(1/t)\) convergence rate of the LQP prediction–correction method. Optim Lett 8, 319–328 (2014). https://doi.org/10.1007/s11590-012-0576-3

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  • DOI: https://doi.org/10.1007/s11590-012-0576-3

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