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A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices

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Abstract

Motivated by the modulus-based Newton method for solving linear complementarity problems (Zheng and Li, J. Comput. Appl. Math. 288, 116–126 2015; Wu and Li, Calcolo 54, 43–56 2017), we propose a generalized modulus-based Newton method to solve a class of non-linear complementarity problems with P-matrices. A sufficient condition to guarantee the convergence of the proposed method is obtained. Numerical experiments further demonstrate that the proposed method is efficient and has better performance than the existing modulus-based iteration method and the Newton method.

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Acknowledgements

The authors are very indebted to the anonymous referees for their helpful comments and valuable suggestions, which have improved the presentation of this paper signicantly. This work is completed while the first author visited North Carolina State University.

Funding

This study is funded by the China Scholarship Council with file number being 201808330668 and the National Natural Science Foundation of China under grant no. 11701221. The third author is funded by the National Natural Science Foundation of China under grant no. 11971354.

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Authors and Affiliations

  1. College of Data Science, Jiaxing University, Zhejiang, 314001, People’s Republic of China

    Rui Li

  2. Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Zhi-Lin Li

  3. School of Mathematical Sciences, Tongji University, Shanghai, 200092, People’s Republic of China

    Jun-Feng Yin

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  1. Rui Li
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  2. Zhi-Lin Li
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  3. Jun-Feng Yin
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Correspondence to Rui Li.

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Li, R., Li, ZL. & Yin, JF. A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices. Numer Algor 89, 839–853 (2022). https://doi.org/10.1007/s11075-021-01136-3

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