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Strong convergence properties of a modified nonmonotone smoothing algorithm for the SCCP

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Abstract

The smoothing algorithms have been successfully applied to solve the symmetric cone complementarity problem (denoted by SCCP), which in general have the global and local superlinear/quadratic convergence if the solution set of the SCCP is nonempty and bounded. Huang, Hu and Han [Science in China Series A: Mathematics, 52: 833–848, 2009] presented a nonmonotone smoothing algorithm for solving the SCCP, whose global convergence is established by just requiring that the solution set of the SCCP is nonempty. In this paper, we propose a new nonmonotone smoothing algorithm for solving the SCCP by modifying the version of Huang-Hu-Han’s algorithm. We prove that the modified nonmonotone smoothing algorithm not only is globally convergent but also has local superlinear/quadratical convergence if the solution set of the SCCP is nonempty. This convergence result is stronger than those obtained by most smoothing-type algorithms. Finally, some numerical results are reported.

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Acknowledgements

The authors are grateful to the referees for their valuable suggestions that improved the paper greatly. This work was supported by National Natural Science Foundation of China (11371306, 11101248, 11271233), Basic and Frontier Technology Research Project of Henan Province (162300410071), Shandong Province Natural Science Foundation (ZR2016AM06, ZR2016AM07), Nanhu Scholars Program for Young Scholars of Xinyang Normal University and Young Teacher Support Program of Shandong University of Technology.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, China

    Jingyong Tang

  2. Department of Mathematics, School of Science, Shandong University of Technology, Zibo, 255049, China

    Jinchuan Zhou

  3. College of Mathematics and System Science, Taishan University, Tai’an, 271021, China

    Liang Fang

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  1. Jingyong Tang
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  2. Jinchuan Zhou
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  3. Liang Fang
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Correspondence to Jingyong Tang.

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Tang, J., Zhou, J. & Fang, L. Strong convergence properties of a modified nonmonotone smoothing algorithm for the SCCP. Optim Lett 12, 411–424 (2018). https://doi.org/10.1007/s11590-017-1134-9

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  • DOI: https://doi.org/10.1007/s11590-017-1134-9

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