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The selection of the optimal parameter in the modulus-based matrix splitting algorithm for linear complementarity problems

Author

Listed:
  • Zhizhi Li

    (Shenzhen University
    University of Chinese Academy of Sciences)

  • Huai Zhang

    (University of Chinese Academy of Sciences)

  • Le Ou-Yang

    (Shenzhen University
    Shenzhen Institute of Artificial Intelligence and Robotics for Society)

Abstract

The modulus-based matrix splitting (MMS) algorithm is effective to solve linear complementarity problems (Bai in Numer Linear Algebra Appl 17: 917–933, 2010). This algorithm is parameter dependent, and previous studies mainly focus on giving the convergence interval of the iteration parameter. Yet the specific selection approach of the optimal parameter has not been systematically studied due to the nonlinearity of the algorithm. In this work, we first propose a novel and simple strategy for obtaining the optimal parameter of the MMS algorithm by merely solving two quadratic equations in each iteration. Further, we figure out the interval of optimal parameter which is iteration independent and give a practical choice of optimal parameter to avoid iteration-based computations. Compared with the experimental optimal parameter, the numerical results from three problems, including the Signorini problem of the Laplacian, show the feasibility, effectiveness and efficiency of the proposed strategy.

Suggested Citation

  • Zhizhi Li & Huai Zhang & Le Ou-Yang, 2021. "The selection of the optimal parameter in the modulus-based matrix splitting algorithm for linear complementarity problems," Computational Optimization and Applications, Springer, vol. 80(2), pages 617-638, November.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:2:d:10.1007_s10589-021-00309-z
    DOI: 10.1007/s10589-021-00309-z
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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.
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