IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v369y2020ics0096300319308823.html
   My bibliography  Save this article

On convergence of the modulus-based matrix splitting iteration method for horizontal linear complementarity problems of H+-matrices

Author

Listed:
  • Zheng, Hua
  • Vong, Seakweng

Abstract

Horizontal linear complementarity problem has wide applications, such as in mechanical and electrical engineering, structural mechanics, piecewise linear system, telecommunication systems and so on. In this paper, we focus on the convergence conditions of the modulus-based matrix splitting iteration method proposed recently for solving horizontal linear complementarity problems. By the proposed theorems, the assumptions on the matrix splitting and the system matrices are weakened, and the convergence domain is enlarged. Numerical examples are presented to show the improvement.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308823
    DOI: 10.1016/j.amc.2019.124890
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319308823
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.124890?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. B. C. Eaves & C. E. Lemke, 1981. "Equivalence of LCP and PLS," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 475-484, November.
    3. Xia, Zechen & Li, Chenliang, 2015. "Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 34-42.
    4. Yinyu Ye, 1993. "A Fully Polynomial-Time Approximation Algorithm for Computing a Stationary Point of the General Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 334-345, May.
    5. H. Saberi Najafi & S. A. Edalatpanah, 2013. "On the Convergence Regions of Generalized Accelerated Overrelaxation Method for Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 859-866, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cuixia Li & Shiliang Wu, 2023. "An Improved Convergence Condition of the MMS Iteration Method for Horizontal LCP of H + -Matrices," Mathematics, MDPI, vol. 11(8), pages 1-6, April.
    2. 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).
    3. Zheng, Hua & Vong, Seakweng, 2021. "On the modulus-based successive overrelaxation iteration method for horizontal linear complementarity problems arising from hydrodynamic lubrication," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Zhang, Yongxiong & Zheng, Hua & Lu, Xiaoping & Vong, Seakweng, 2023. "Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    3. Dongmei Yu & Huiling Wei & Cairong Chen & Deren Han, 2024. "Scalable Relaxation Two-Sweep Modulus-Based Matrix Splitting Methods for Vertical LCP," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 714-744, October.
    4. J. Z. Zhang & N. H. Xiu, 1999. "Local Uniqueness of Solutions to the Extended Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 715-726, December.
    5. Joaquim Júdice, 2012. "Algorithms for linear programming with linear complementarity constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 4-25, April.
    6. 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.
    7. Ping-Fan Dai & Shi-Liang Wu, 2022. "The GUS-Property and Modulus-Based Methods for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 976-1006, December.
    8. Cuixia Li & Shiliang Wu, 2023. "An Improved Convergence Condition of the MMS Iteration Method for Horizontal LCP of H + -Matrices," Mathematics, MDPI, vol. 11(8), pages 1-6, April.
    9. Baohua Huang & Wen Li, 2023. "A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 345-381, September.
    10. Zheng, Hua & Vong, Seakweng & Liu, Ling, 2019. "A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 396-405.
    11. 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.
    12. Hua Zheng & Ling Liu, 2019. "The Sign-Based Methods for Solving a Class of Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 480-499, February.
    13. Bharat Kumar & Deepmala & A. Dutta & A. K. Das, 2023. "More on matrix splitting modulus-based iterative methods for solving linear complementarity problem," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 1003-1020, June.
    14. 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.
    15. Apostolos Hadjidimos & Michael Tzoumas, 2015. "On the Solution of the Linear Complementarity Problem by the Generalized Accelerated Overrelaxation Iterative Method," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 545-562, May.
    16. Srihari Govindan & Robert Wilson, 2006. "Metastable Equilibria," Levine's Bibliography 122247000000001211, UCLA Department of Economics.
    17. Zhang, Li-Li, 2021. "A modulus-based multigrid method for nonlinear complementarity problems with application to free boundary problems with nonlinear source terms," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    18. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308823. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.