IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i2p168-d314562.html
   My bibliography  Save this article

A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations

Author

Listed:
  • Zhifeng Dai

    (College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China)

  • Huan Zhu

    (College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China)

Abstract

The goal of this paper is to extend the modified Hestenes-Stiefel method to solve large-scale nonlinear monotone equations. The method is presented by combining the hyperplane projection method (Solodov, M.V.; Svaiter, B.F. A globally convergent inexact Newton method for systems of monotone equations, in: M. Fukushima, L. Qi (Eds.)Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publishers. 1998, 355-369) and the modified Hestenes-Stiefel method in Dai and Wen (Dai, Z.; Wen, F. Global convergence of a modified Hestenes-Stiefel nonlinear conjugate gradient method with Armijo line search. Numer Algor. 2012, 59, 79-93). In addition, we propose a new line search for the derivative-free method. Global convergence of the proposed method is established if the system of nonlinear equations are Lipschitz continuous and monotone. Preliminary numerical results are given to test the effectiveness of the proposed method.

Suggested Citation

  • Zhifeng Dai & Huan Zhu, 2020. "A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations," Mathematics, MDPI, vol. 8(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:168-:d:314562
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/2/168/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/2/168/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yilun Shang, 2019. "Super Connectivity of Erdős-Rényi Graphs," Mathematics, MDPI, vol. 7(3), pages 1-5, 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. Dai, Zhifeng & Luo, Zhuang & Liu, Chang, 2023. "Dynamic volatility spillovers and investment strategies between crude oil, new energy, and resource related sectors," Resources Policy, Elsevier, vol. 83(C).
    2. Eltiyeb Ali & Salem Mahdi, 2023. "Adaptive Hybrid Mixed Two-Point Step Size Gradient Algorithm for Solving Non-Linear Systems," Mathematics, MDPI, vol. 11(9), pages 1-35, April.
    3. Dai, Zhifeng & Tang, Rui & Zhang, Xiaotong, 2023. "A new multilayer network for measuring interconnectedness among the energy firms," Energy Economics, Elsevier, vol. 124(C).

    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.

      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:gam:jmathe:v:8:y:2020:i:2:p:168-:d:314562. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.