IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v133y2007i3d10.1007_s10957-007-9238-5.html
   My bibliography  Save this article

On the Surrogate Gradient Algorithm for Lagrangian Relaxation

Author

Listed:
  • T. Sun

    (Tsinghua University)

  • Q. C. Zhao

    (Tsinghua University)

  • P. B. Luh

    (Tsinghua University
    University of Connecticut)

Abstract

When applied to large-scale separable optimization problems, the recently developed surrogate subgradient method for Lagrangian relaxation (Zhao et al.: J. Optim. Theory Appl. 100, 699–712, 1999) does not need to solve optimally all the subproblems to update the multipliers, as the traditional subgradient method requires. Based on it, the penalty surrogate subgradient algorithm was further developed to address the homogenous solution issue (Guan et al.: J. Optim. Theory Appl. 113, 65–82, 2002; Zhai et al.: IEEE Trans. Power Syst. 17, 1250–1257, 2002). There were flaws in the proofs of Zhao et al., Guan et al., and Zhai et al.: for problems with inequality constraints, projection is necessary to keep the multipliers nonnegative; however, the effects of projection were not properly considered. This note corrects the flaw, completes the proofs, and asserts the correctness of the methods.

Suggested Citation

  • T. Sun & Q. C. Zhao & P. B. Luh, 2007. "On the Surrogate Gradient Algorithm for Lagrangian Relaxation," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 413-416, June.
  • Handle: RePEc:spr:joptap:v:133:y:2007:i:3:d:10.1007_s10957-007-9238-5
    DOI: 10.1007/s10957-007-9238-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9238-5
    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/s10957-007-9238-5?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. Mikhail A. Bragin & Peter B. Luh & Joseph H. Yan & Nanpeng Yu & Gary A. Stern, 2015. "Convergence of the Surrogate Lagrangian Relaxation Method," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 173-201, January.
    2. Azadian, Farshid & Murat, Alper & Chinnam, Ratna Babu, 2015. "Integrated production and logistics planning: Contract manufacturing and choice of air/surface transportation," European Journal of Operational Research, Elsevier, vol. 247(1), pages 113-123.

    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:133:y:2007:i:3:d:10.1007_s10957-007-9238-5. 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.