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Weighted max-norm estimate of two-stage splitting method for solving a class of nonlinear complementarity problems

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Abstract

In this paper, we consider the splitting method and the two-stage splitting method for solving a class of nonlinear complementarity problems with the coefficient matrix being an \(H\)-matrix. Convergence result for the splitting method is presented when the splitting is \(H\)-splitting. Moreover, for the two-stage splitting method, we estimate weighted max-norm bounds for iteration errors, and thereby, we show that the sequence generated by the two-stage iteration scheme converges to the unique solution of the nonlinear complementarity problem without any restriction on the initial vector. Numerical results show that both methods are efficient for solving the class of nonlinear complementarity problems.

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Acknowledgments

The authors would like to express their appreciations to the anonymous reviewers for the invaluable comments that have greatly improved the quality of the manuscript.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Haijian Yang & Qingguo Li

  2. College of Mechanical Engineering, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Jingang Liu

Authors
  1. Haijian Yang
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  2. Qingguo Li
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  3. Jingang Liu
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Corresponding author

Correspondence to Haijian Yang.

Additional information

This research was supported in part by NSFC under Grants 11201137, 11272352, and 91330111, in part by the Hunan Provincial Natural Science Foundation of China under Grant 12JJ4002. J. Liu was also supported in part by the Hunan Provincial Natural Science Foundation of China Grant 13JJ8005.

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Yang, H., Li, Q. & Liu, J. Weighted max-norm estimate of two-stage splitting method for solving a class of nonlinear complementarity problems. Neural Comput & Applic 25, 937–944 (2014). https://doi.org/10.1007/s00521-014-1580-6

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  • DOI: https://doi.org/10.1007/s00521-014-1580-6

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