IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v311y2017icp195-202.html
   My bibliography  Save this article

SOR-like iteration method for solving absolute value equations

Author

Listed:
  • Ke, Yi-Fen
  • Ma, Chang-Feng

Abstract

In this paper, we propose an SOR-like iteration method for solving the absolute value equation (AVE), which is obtained by reformulating equivalently the AVE as a two-by-two block nonlinear equation. The convergence results of the proposed iteration method are proved under certain assumptions imposed on the involved parameter. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the SOR-like iteration method.

Suggested Citation

  • Ke, Yi-Fen & Ma, Chang-Feng, 2017. "SOR-like iteration method for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 195-202.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:195-202
    DOI: 10.1016/j.amc.2017.05.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317303363
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.05.035?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. Louis Caccetta & Biao Qu & Guanglu Zhou, 2011. "A globally and quadratically convergent method for absolute value equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 45-58, January.
    2. J. Y. Bello Cruz & O. P. Ferreira & L. F. Prudente, 2016. "On the global convergence of the inexact semi-smooth Newton method for absolute value equation," Computational Optimization and Applications, Springer, vol. 65(1), pages 93-108, September.
    3. Edalatpour, Vahid & Hezari, Davod & Khojasteh Salkuyeh, Davod, 2017. "A generalization of the Gauss–Seidel iteration method for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 156-167.
    4. Moosaei, H. & Ketabchi, S. & Noor, M.A. & Iqbal, J. & Hooshyarbakhsh, V., 2015. "Some techniques for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 696-705.
    5. Zhang, Jian-Jun, 2015. "The relaxed nonlinear PHSS-like iteration method for absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 266-274.
    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. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, 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. Milan Hladík, 2018. "Bounds for the solutions of absolute value equations," Computational Optimization and Applications, Springer, vol. 69(1), pages 243-266, January.
    2. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    3. Cui-Xia Li, 2016. "A Modified Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1055-1059, September.
    4. An Wang & Yang Cao & Jing-Xian Chen, 2019. "Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 216-230, April.
    5. Shota Yamanaka & Nobuo Yamashita, 2018. "Duality of nonconvex optimization with positively homogeneous functions," Computational Optimization and Applications, Springer, vol. 71(2), pages 435-456, November.
    6. Butyn, Emerson & Karas, Elizabeth W. & de Oliveira, Welington, 2022. "A derivative-free trust-region algorithm with copula-based models for probability maximization problems," European Journal of Operational Research, Elsevier, vol. 298(1), pages 59-75.
    7. J. Y. Bello Cruz & O. P. Ferreira & L. F. Prudente, 2016. "On the global convergence of the inexact semi-smooth Newton method for absolute value equation," Computational Optimization and Applications, Springer, vol. 65(1), pages 93-108, September.
    8. Peng Guo & Javed Iqbal & Syed Muhammad Ghufran & Muhammad Arif & Reem K. Alhefthi & Lei Shi, 2023. "A New Efficient Method for Absolute Value Equations," Mathematics, MDPI, vol. 11(15), pages 1-9, July.
    9. Miao, Xin-He & Yang, Jiantao & Hu, Shenglong, 2015. "A generalized Newton method for absolute value equations associated with circular cones," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 155-168.
    10. Juan Yin & Qingna Li, 2019. "A semismooth Newton method for support vector classification and regression," Computational Optimization and Applications, Springer, vol. 73(2), pages 477-508, June.
    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. Zhang, Jian-Jun, 2015. "The relaxed nonlinear PHSS-like iteration method for absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 266-274.
    13. Hossein Moosaei & Saeed Ketabchi & Milan Hladík, 2021. "Optimal correction of the absolute value equations," Journal of Global Optimization, Springer, vol. 79(3), pages 645-667, March.
    14. Fabiana R. Oliveira & Fabrícia R. Oliveira, 2021. "A Global Newton Method for the Nonsmooth Vector Fields on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 259-273, July.
    15. Shi-Liang Wu & Peng Guo, 2016. "On the Unique Solvability of the Absolute Value Equation," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 705-712, May.
    16. Cuixia Li, 2022. "Sufficient Conditions for the Unique Solution of a New Class of Sylvester-Like Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 676-683, November.

    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:311:y:2017:i:c:p:195-202. 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.