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A relaxation two-step parallel modulus method without auxiliary variable for solving large sparse vertical linear complementarity problems

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Abstract

In this work, for solving large sparse vertical linear complementarity problems, a relaxation two-step modulus-based synchronous multisplitting method without auxiliary variable is constructed. The convergence conditions are presented for the proposed method, where the range of the relaxation parameters is obtained. By OpenACC framework, the proposed method is shown to be more efficient than the existing method with high speedups with numerical tests.

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Data Availability

There is no availability of supporting data. All numerical test data are stated in Section 4.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments.

Funding

This work was supported by Scientific Computing Research Innovation Team of Guangdong Province (No. 2021KCXTD052), Science and Technology Development Fund, Macau SAR (No. 0096/2022/A, 0151/2022/A), University of Macau (No. MYRG2022-00076-FST, MYRG-GRG2023-00037-FST-UMDF), Guangdong Key Construction Discipline Research Capacity Enhancement Project (No. 2022ZDJS049), Characteristic innovation project of Guangdong Provincial Department of Education (No. 2023KTSCX195), Technology Planning Project of Shaoguan (No. 230330108034184), and Guangdong Basic and Applied Basic Research Foundation (No. 2024A1515011822).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Macau University of Science and Technology, Macau, People’s Republic of China

    Wenxiu Guo, Xiaoping Lu & Yongxiong Zhang

  2. School of Mathematics and Statistics, Shaoguan University, Shaoguan, People’s Republic of China

    Wenxiu Guo & Hua Zheng

  3. School of Engineering, Guangzhou College of Technology and Business, Guangzhou, People’s Republic of China

    Yongxiong Zhang

  4. Department of Mathematics, University of Macau, Macau, People’s Republic of China

    Seakweng Vong

Authors
  1. Wenxiu Guo
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  2. Hua Zheng
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  3. Xiaoping Lu
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  4. Yongxiong Zhang
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  5. Seakweng Vong
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Contributions

Guo W. designed the new method and completed the convergence analysis. Zheng H. provided the main idea of the proof in convergence analysis. Lu X. constructed the OpenACC framework for all numerical examples and designed the original C codes. Zhang Y. completed the numerical tests and wrote the section of numerical examples. Vong S. checked the mathematics and English writing throughout the manuscript.

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Correspondence to Xiaoping Lu.

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Guo, W., Zheng, H., Lu, X. et al. A relaxation two-step parallel modulus method without auxiliary variable for solving large sparse vertical linear complementarity problems. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01800-4

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