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Splitting Methods for a Class of Horizontal Linear Complementarity Problems

Author

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  • Francesco Mezzadri

    (University of Modena and Reggio Emilia)

  • Emanuele Galligani

    (University of Modena and Reggio Emilia)

Abstract

In this paper, we propose two splitting methods for solving horizontal linear complementarity problems characterized by matrices with positive diagonal elements. The proposed procedures are based on the Jacobi and on the Gauss–Seidel iterations and differ from existing techniques in that they act directly and simultaneously on both matrices of the problem. We prove the convergence of the methods under some assumptions on the diagonal dominance of the matrices of the problem. Several numerical experiments, including large-scale problems of practical interest, demonstrate the capabilities of the proposed methods in various situations.

Suggested Citation

  • Francesco Mezzadri & Emanuele Galligani, 2019. "Splitting Methods for a Class of Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 500-517, February.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1395-1
    DOI: 10.1007/s10957-018-1395-1
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    Cited by:

    1. Mezzadri, Francesco & Galligani, Emanuele, 2020. "On the convergence of modulus-based matrix splitting methods for horizontal linear complementarity problems in hydrodynamic lubrication," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 226-242.
    2. Zheng, Hua & Vong, Seakweng, 2020. "On convergence of the modulus-based matrix splitting iteration method for horizontal linear complementarity problems of H+-matrices," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    3. Zhang, Yongxiong & Zheng, Hua & Vong, Seakweng & Lu, Xiaoping, 2023. "A two-step parallel iteration method for large sparse horizontal linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    4. Punit Kumar Yadav & Palpandi Karuppaiah, 2023. "Generalizations of $$R_0$$ R 0 and $$\textbf{SSM}$$ SSM Properties for Extended Horizontal Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 392-414, October.
    5. Francesco Mezzadri & Emanuele Galligani, 2022. "Projected Splitting Methods for Vertical Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 598-620, June.
    6. Chen Sun & Yong Wang & Zheng-Hai Huang, 2024. "An Iterative Method for Horizontal Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 854-877, August.

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