IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v180y2019i2d10.1007_s10957-018-1361-y.html
   My bibliography  Save this article

The Sign-Based Methods for Solving a Class of Nonlinear Complementarity Problems

Author

Listed:
  • Hua Zheng

    (Shaoguan University)

  • Ling Liu

    (Shaoguan University)

Abstract

In this paper, using the sign patterns of the solution of the equivalent modulus equation, the resolution of the nonlinear complementarity problem shrinks to find the zero of a differentiable nonlinear function. Then, a sign-based Newton’s method is established by applying the Newton’s iteration. The theoretical analysis for the sign patterns of the solution of the equivalent modulus equation is given under the assumption of strictly complementarity. Moreover, by using the known modulus-based matrix splitting iteration method to detect the sign patterns of the solution of the equivalent modulus equation, a practical sign-detection Newton’s method is proposed. Numerical examples show that the new methods are efficient and accelerate the convergence performance with higher precision and less CPU time than the existing modulus-based matrix splitting iteration method and the projection-based matrix splitting iteration method, especially for the large sparse problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1361-y
    DOI: 10.1007/s10957-018-1361-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1361-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-018-1361-y?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. Wen, Baolian & Zheng, Hua & Li, Wen & Peng, Xiaofei, 2018. "The relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems of positive definite matrices," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 349-357.
    2. 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.
    3. Li-Li Zhang, 2014. "Two-Stage Multisplitting Iteration Methods Using Modulus-Based Matrix Splitting as Inner Iteration for Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 189-203, January.
    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. Yiyin Cao & Chuangyin Dang & Yabin Sun, 2022. "Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 533-563, February.

    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. 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.
    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. 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.
    4. 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).
    5. 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.
    6. 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.
    7. Guo, Wenxiu & Zheng, Hua & Lu, Xiaoping & Zhang, Yongxiong, 2024. "On the two-stage multisplitting iteration methods for linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    8. 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.
    9. Zhizhi Li & Huai Zhang & Le Ou-Yang, 2021. "The selection of the optimal parameter in the modulus-based matrix splitting algorithm for linear complementarity problems," Computational Optimization and Applications, Springer, vol. 80(2), pages 617-638, November.
    10. 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).
    11. 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).
    12. 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).
    13. Zhang, Xu & Peng, Zheng, 2020. "A modulus-based nonmonotone line search method for nonlinear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 387(C).

    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:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1361-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.