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A smoothing Levenberg-Marquardt method for nonlinear complementarity problems

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Abstract

As is well-known, Jacobian smoothing method is a popular one to solve nonlinear complementarity problems, in which the Jacobian consistency is stressed. By investigating an element of related functions’ B-differential, a smoothing Levenberg-Marquardt(LM) method is proposed based on a Chen-Harker-Kanzow-Smale(CHKS) smoothing function, which satisfies a property called strongly Jacobian consistency. Finally, the numerical experiments illustrate the effectiveness of the given method.

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Acknowledgments

The authors are grateful to the anonymous referees for their helpful comments and suggestions.

Funding

This work was supported by the National Science Foundation of China (no. 11171221), the Research Fund for the Doctoral Program of Higher Education of China (no. 20123120110004), the Natural Science Foundation of Shanghai (no. 14ZR1429200), and the Innovation Program of Shanghai Municipal Education Commission (no. 15ZZ073).

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Authors and Affiliations

  1. School of Management, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Linsen Song & Yan Gao

  2. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, 453003, China

    Linsen Song

Authors
  1. Linsen Song
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  2. Yan Gao
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Correspondence to Yan Gao.

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Song, L., Gao, Y. A smoothing Levenberg-Marquardt method for nonlinear complementarity problems. Numer Algor 79, 1305–1321 (2018). https://doi.org/10.1007/s11075-018-0485-3

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  • DOI: https://doi.org/10.1007/s11075-018-0485-3

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