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

Zhizhi Li (), Huai Zhang and Le Ou-Yang ()
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Zhizhi Li: Shenzhen University
Huai Zhang: University of Chinese Academy of Sciences
Le Ou-Yang: Shenzhen University

Computational Optimization and Applications, 2021, vol. 80, issue 2, No 10, 617-638

Abstract: 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.

Keywords: Optimal parameter; Practical solution; Quadratic equation; Modulus-based matrix splitting; Linear complementarity problems; 65H10; 90C33 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10589-021-00309-z

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