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An efficient modulus-based matrix splitting iteration method for quasi-complementarity problems

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Abstract

In this paper, by transforming the quasi-complementarity problem (QCP) into an equivalent fixed-point format, we develop an efficient modulus-based matrix splitting (EMMS) iteration method for the large sparse QCPs. Compared with the MMS (Appl. Numer. Math. 55:8, 2018) and the TMMS (Comput. Appl. Math. 39:11, 2020) methods, the EMMS iteration method does not involve inner iterations and its initial vector can be chosen unlimitedly. Thus, the EMMS method may be more efficient than some existing ones in the practical calculation. And we prove that the EMMS iteration method is convergent under mild conditions when the system matrices are either positive definite matrices or \(H_{+}\)-matrices, which generalize some known corresponding results. Besides, the convergence of the EM accelerated overrelaxation (EMAOR) method has also been analyzed, which is practical in real calculation. Lastly, several numerical examples are provided to show that the EMMS method is effective and feasible.

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Acknowledgements

We would like to express our sincere thanks to editor and anonymous reviewer for their valuable suggestions and constructive comments which greatly improved the presentation of this paper.

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Authors and Affiliations

  1. College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, People’s Republic of China

    Zhengge Huang & Jingjing Cui

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  1. Zhengge Huang
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  2. Jingjing Cui
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Correspondence to Zhengge Huang.

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Communicated by Gabriel Haeser.

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This work was supported by the National Science Foundation of China (No. 11901123), the Guangxi Natural Science Foundations (No. 2018JJB110062, 2019AC20062, 2021JJB110006, 2021AC19147), and the Natural Science Foundation of Guangxi University for Nationalities (No. 2019KJQN001).

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Huang, Z., Cui, J. An efficient modulus-based matrix splitting iteration method for quasi-complementarity problems. Comp. Appl. Math. 41, 296 (2022). https://doi.org/10.1007/s40314-022-02011-0

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