IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v149y2011i2d10.1007_s10957-010-9782-2.html
   My bibliography  Save this article

On the Solution of Generalized Multiplicative Extremum Problems

Author

Listed:
  • Alireza M. Ashtiani

    (State University of Campinas)

  • Paulo A. V. Ferreira

    (State University of Campinas)

Abstract

The paper addresses the problem of maximizing a sum of products of positive and concave real-valued functions over a convex feasible set. A reformulation based on the image of the feasible set through the vector-valued function which describes the problem, combined with an adequate application of convex analysis results, lead to an equivalent indefinite quadratic extremum problem with infinitely many linear constraints. Special properties of this later problem allow to solve it by an efficient relaxation algorithm. Some numerical tests illustrate the approach proposed.

Suggested Citation

  • Alireza M. Ashtiani & Paulo A. V. Ferreira, 2011. "On the Solution of Generalized Multiplicative Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 411-419, May.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:2:d:10.1007_s10957-010-9782-2
    DOI: 10.1007/s10957-010-9782-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9782-2
    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/s10957-010-9782-2?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. Rúbia Oliveira & Paulo Ferreira, 2010. "An outcome space approach for generalized convex multiplicative programs," Journal of Global Optimization, Springer, vol. 47(1), pages 107-118, May.
    2. H. P. Benson, 2008. "Global Maximization of a Generalized Concave Multiplicative Function," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 105-120, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Ashtiani, Alireza M. & Ferreira, Paulo A.V., 2015. "A branch-and-cut algorithm for a class of sum-of-ratios problems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 596-608.

    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. Peiping Shen & Kaimin Wang & Ting Lu, 2020. "Outer space branch and bound algorithm for solving linear multiplicative programming problems," Journal of Global Optimization, Springer, vol. 78(3), pages 453-482, November.
    2. Peiping Shen & Dianxiao Wu & Kaimin Wang, 2023. "Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound," Journal of Global Optimization, Springer, vol. 86(2), pages 303-321, June.
    3. Ashtiani, Alireza M. & Ferreira, Paulo A.V., 2015. "A branch-and-cut algorithm for a class of sum-of-ratios problems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 596-608.
    4. Rúbia Oliveira & Paulo Ferreira, 2010. "An outcome space approach for generalized convex multiplicative programs," Journal of Global Optimization, Springer, vol. 47(1), pages 107-118, 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:149:y:2011:i:2:d:10.1007_s10957-010-9782-2. 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.