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A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems

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Abstract

By equivalently transforming a class of weakly nonlinear complementarity problems into a modulus equation, and introducing a smoothing approximation of the absolute value function, a smoothing Newton method is established for solving the weakly nonlinear complementarity problem. Under some mild assumptions, the proposed method is shown to possess global convergence and locally quadratical convergence. Especially, the global convergence results do not need a priori existence of an accumulation point with some suitable conditions. Numerical results are given to show the efficiency of the proposed method.

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Acknowledgements

The authors would like to thank the editor and anonymous referees whose comments and suggestions have greatly improved the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, People’s Republic of China

    Baohua Huang

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Wen Li

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  1. Baohua Huang
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  2. Wen Li
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Correspondence to Wen Li.

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The first author is supported by National Natural Science Foundation of China (12001211, 12071159, 12171168) and Natural Science Foundation of Fujian Province, China (2022J01194). The second author is supported by National Natural Science Foundation of China (12071159, U1811464).

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Huang, B., Li, W. A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems. Comput Optim Appl 86, 345–381 (2023). https://doi.org/10.1007/s10589-023-00482-3

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