IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v113y2002i1d10.1023_a1014801112646.html
   My bibliography  Save this article

Comparison of Two Sets of First-Order Conditions as Bases of Interior-Point Newton Methods for Optimization with Simple Bounds

Author

Listed:
  • D.C. Jamrog

    (Rice University)

  • R.A. Tapia

    (Rice University)

  • Y. Zhang

    (Rice University)

Abstract

In this paper, we compare the behavior of two Newton interior-point methods derived from two different first-order necessary conditions for the same nonlinear optimization problem with simple bounds. One set of conditions was proposed by Coleman and Li; the other is the standard KKT set of conditions. We discuss a perturbation of the CL conditions for problems with one-sided bounds and the difficulties involved in extending this to problems with general bounds. We study the numerical behavior of the Newton method applied to the systems of equations associated with the unperturbed and perturbed necessary conditions. Preliminary numerical results for convex quadratic objective functions indicate that, for this class of problems, the Newton method based on the perturbed KKT formulation appears to be the more robust.

Suggested Citation

  • D.C. Jamrog & R.A. Tapia & Y. Zhang, 2002. "Comparison of Two Sets of First-Order Conditions as Bases of Interior-Point Newton Methods for Optimization with Simple Bounds," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 21-40, April.
    • Handle: RePEc:spr:joptap:v:113:y:2002:i:1:d:10.1023_a:1014801112646
    DOI: 10.1023/A:1014801112646
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1014801112646
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1014801112646?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. C. Villalobos & R. Tapia & Y. Zhang, 2002. "Local Behavior of the Newton Method on Two Equivalent Systems from Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 239-263, February.
    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. M. C. Villalobos & R. A. Tapia & Y. Zhang, 2004. "Sphere of Convergence of Newton's Method on Two Equivalent Systems from Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 489-514, June.
    2. L. A. Melara & A. J. Kearsley & R. A. Tapia, 2007. "Augmented Lagrangian Homotopy Method for the Regularization of Total Variation Denoising Problems," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 15-25, 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:joptap:v:113:y:2002:i:1:d:10.1023_a:1014801112646. 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.