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A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices

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  • Zheng, Hua
  • Vong, Seakweng
  • Liu, Ling

Abstract

In this paper, we establish a direct preconditioned modulus-based iteration method for solving a class of nonlinear complementarity problems with the system matrix being an H-matrix. The convergence theorems of the proposed method are given, which generalize and improve the existing ones. Numerical examples show that the proposed method is efficient.

Suggested Citation

  • Zheng, Hua & Vong, Seakweng & Liu, Ling, 2019. "A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 396-405.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:396-405
    DOI: 10.1016/j.amc.2019.02.015
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    References listed on IDEAS

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    1. Wen, Baolian & Zheng, Hua & Li, Wen & Peng, Xiaofei, 2018. "The relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems of positive definite matrices," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 349-357.
    2. Xia, Zechen & Li, Chenliang, 2015. "Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 34-42.
    3. Li-Li Zhang, 2014. "Two-Stage Multisplitting Iteration Methods Using Modulus-Based Matrix Splitting as Inner Iteration for Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 189-203, January.
    4. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. Zhang, Li-Li, 2021. "A modulus-based multigrid method for nonlinear complementarity problems with application to free boundary problems with nonlinear source terms," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    2. Zheng, Hua & Vong, Seakweng, 2021. "On the modulus-based successive overrelaxation iteration method for horizontal linear complementarity problems arising from hydrodynamic lubrication," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    3. Baohua Huang & Wen Li, 2023. "A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 345-381, September.

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