IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v92y1997i1d10.1023_a1022690711754.html
   My bibliography  Save this article

Family of Projected Descent Methods for Optimization Problems with Simple Bounds

Author

Listed:
  • A. Schwartz

    (University of California)

  • E. Polak

    (University of California)

Abstract

This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems.

Suggested Citation

  • A. Schwartz & E. Polak, 1997. "Family of Projected Descent Methods for Optimization Problems with Simple Bounds," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 1-31, January.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:1:d:10.1023_a:1022690711754
    DOI: 10.1023/A:1022690711754
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022690711754
    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:1022690711754?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Johannes O. Royset, 2016. "Preface," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 713-718, June.
    2. Cristofari, Andrea, 2023. "A decomposition method for lasso problems with zero-sum constraint," European Journal of Operational Research, Elsevier, vol. 306(1), pages 358-369.
    3. Denis Becker & Alexei Gaivoronski, 2014. "Stochastic optimization on social networks with application to service pricing," Computational Management Science, Springer, vol. 11(4), pages 531-562, October.
    4. M. Santis & G. Pillo & S. Lucidi, 2012. "An active set feasible method for large-scale minimization problems with bound constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 395-423, October.
    5. N.H. Xiu & J.Z. Zhang, 2002. "Local Convergence Analysis of Projection-Type Algorithms: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 211-230, October.
    6. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2017. "A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 369-401, February.
    7. Hoai Le Thi & Van Huynh & Tao Dinh & A. Vaz & L. Vicente, 2014. "Globally convergent DC trust-region methods," Journal of Global Optimization, Springer, vol. 59(2), pages 209-225, July.
    8. David Ek & Anders Forsgren, 2021. "Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization," Computational Optimization and Applications, Springer, vol. 79(1), pages 155-191, May.

    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:92:y:1997:i:1:d:10.1023_a:1022690711754. 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.