IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v66y2017i3d10.1007_s10589-016-9878-1.html
   My bibliography  Save this article

Partitioned quasi-Newton methods for sparse nonlinear equations

Author

Listed:
  • Hui-Ping Cao

    (Hunan University)

  • Dong-Hui Li

    (South China Normal University)

Abstract

In this paper, we present two partitioned quasi-Newton methods for solving partially separable nonlinear equations. When the Jacobian is not available, we propose a partitioned Broyden’s rank one method and show that the full step partitioned Broyden’s rank one method is locally and superlinearly convergent. By using a well-defined derivative-free line search, we globalize the method and establish its global and superlinear convergence. In the case where the Jacobian is available, we propose a partitioned adjoint Broyden method and show its global and superlinear convergence. We also present some preliminary numerical results. The results show that the two partitioned quasi-Newton methods are effective and competitive for solving large-scale partially separable nonlinear equations.

Suggested Citation

  • Hui-Ping Cao & Dong-Hui Li, 2017. "Partitioned quasi-Newton methods for sparse nonlinear equations," Computational Optimization and Applications, Springer, vol. 66(3), pages 481-505, April.
    • Handle: RePEc:spr:coopap:v:66:y:2017:i:3:d:10.1007_s10589-016-9878-1
    DOI: 10.1007/s10589-016-9878-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-016-9878-1
    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/s10589-016-9878-1?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. Narges Bidabadi & Nezam Mahdavi-Amiri, 2014. "Superlinearly Convergent Exact Penalty Methods with Projected Structured Secant Updates for Constrained Nonlinear Least Squares," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 154-190, July.
    Full references (including those not matched with items on IDEAS)

    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. Dominique Orban & Abel Soares Siqueira, 2020. "A regularization method for constrained nonlinear least squares," Computational Optimization and Applications, Springer, vol. 76(3), pages 961-989, July.

    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:coopap:v:66:y:2017:i:3:d:10.1007_s10589-016-9878-1. 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.