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

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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.

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Acknowledgements

This work is supported by National Science Foundation of China (Nos. 42004085, 41725017 and 61602309), China Postdoctoral Science Foundation (No. 2019M663040), Guangdong Basic and Applied Basic Research Foundation (Nos. 2019A1515110184 and 2019A1515011384), the National Key R & D Program of the Ministry of Science and Technology of China (No. 2020YFA0713400), and Shenzhen Fundamental Research Program (No. JCYJ20170817095210760).

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Authors and Affiliations

  1. Guangdong Key Laboratory of Intelligent Information Processing and Shenzhen Key Laboratory of Media Security, College of Electronics and Information Engineering, Shenzhen University, Shenzhen, 518060, China

    Zhizhi Li & Le Ou-Yang

  2. Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhizhi Li & Huai Zhang

  3. Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, 518060, China

    Le Ou-Yang

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  1. Zhizhi Li
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  2. Huai Zhang
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  3. Le Ou-Yang
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Correspondence to Le Ou-Yang.

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Li, Z., Zhang, H. & Ou-Yang, L. The selection of the optimal parameter in the modulus-based matrix splitting algorithm for linear complementarity problems. Comput Optim Appl 80, 617–638 (2021). https://doi.org/10.1007/s10589-021-00309-z

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