IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/2003086.html
   My bibliography  Save this paper

Modified Gauss-Newton scheme with worst-case guarantees for its global performance

Author

Listed:
  • NESTEROV, Yu

Abstract

In this paper we suggest a new version of Gauss-Newton method for solving a system of nonlinear equations, which combines the idea of a sharp merit function with the idea of a quadratic regularization. For this scheme we prove general convergence results and, under a natural non-degeneracy assumption, a local quadratic convergence. We analyze the behavior of this scheme on some natural problem class, for which we get global and local worst-case complexity bounds. The implementation of each step of the scheme can be done by a standard convex optimization technique.

Suggested Citation

  • NESTEROV, Yu, 2003. "Modified Gauss-Newton scheme with worst-case guarantees for its global performance," LIDAM Discussion Papers CORE 2003086, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2003086
    as

    Download full text from publisher

    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2003.html
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. NESTEROV, Yurii & POLYAK, Boris, 2003. "Cubic regularization of a Newton scheme and its global performance," LIDAM Discussion Papers CORE 2003041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Polyak, B.T., 2007. "Newton's method and its use in optimization," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1086-1096, September.
    2. NESTEROV, Yu., 2006. "Cubic regularization of Newton’s method for convex problems with constraints," LIDAM Discussion Papers CORE 2006039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    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:cor:louvco:2003086. 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: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    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.