IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v87y2023i2d10.1007_s10898-022-01215-2.html
   My bibliography  Save this article

A derivative-free scaling memoryless DFP method for solving large scale nonlinear monotone equations

Author

Listed:
  • Jiayun Rao

    (China Agricultural University)

  • Na Huang

    (China Agricultural University)

Abstract

Quasi-Newton methods for solving nonlinear system of equations provide an attractive alternative to the Newton method in which they do not require computation of the Jacobian matrix and still possess superlinear convergence. In this paper, we develop a new sufficient descent direction based on a scaling memoryless DFP updating formula. By combining this descent direction with a projection approach, we propose a derivative-free scaling memoryless DFP method for solving nonlinear monotone equations and establish its global convergence under reasonable conditions. In sharp contrast with the original DFP method, our new method does not involve computing matrices. This makes it particularly suitable for solving large scale problems. The presented results of numerical experiments demonstrate the robustness and efficiency of our new method.

Suggested Citation

  • Jiayun Rao & Na Huang, 2023. "A derivative-free scaling memoryless DFP method for solving large scale nonlinear monotone equations," Journal of Global Optimization, Springer, vol. 87(2), pages 641-677, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01215-2
    DOI: 10.1007/s10898-022-01215-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01215-2
    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/s10898-022-01215-2?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.

    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:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01215-2. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.