IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v137y2008i1d10.1007_s10957-007-9332-8.html
   My bibliography  Save this article

Complex Minimax Fractional Programming of Analytic Functions

Author

Listed:
  • H. C. Lai

    (Chung-Yuan Christian University)

  • J. C. Liu

    (National Taiwan Normal University)

  • S. Schaible

    (University of California)

Abstract

We prove that a minmax fractional programming problem is equivalent to a minimax nonfractional parametric problem for a given parameter in complex space. Using a parametric approach, we establish the Kuhn-Tucker type necessary optimality conditions and prove the existence theorem of optimality for complex minimax fractional programming in the framework of generalized convexity. Subsequently, we apply the optimality conditions to formulate a one-parameter dual problem and prove weak duality, strong duality, and strict converse duality theorems involving generalized convex complex functions.

Suggested Citation

  • H. C. Lai & J. C. Liu & S. Schaible, 2008. "Complex Minimax Fractional Programming of Analytic Functions," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 171-184, April.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:1:d:10.1007_s10957-007-9332-8
    DOI: 10.1007/s10957-007-9332-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9332-8
    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/s10957-007-9332-8?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. J. C. Chen & H. C. Lai & S. Schaible, 2005. "Complex Fractional Programming and the Charnes-Cooper Transformation," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 203-213, July.
    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. Hang-Chin Lai & Tone-Yau Huang, 2012. "Nondifferentiable minimax fractional programming in complex spaces with parametric duality," Journal of Global Optimization, Springer, vol. 53(2), pages 243-254, June.
    2. Tone-Yau Huang, 2020. "Second-Order Parametric Free Dualities for Complex Minimax Fractional Programming," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    3. Jiawei Chen & Suliman Al-Homidan & Qamrul Hasan Ansari & Jun Li & Yibing Lv, 2021. "Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 221-243, April.

    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. Laura Carosi & Laura Martein, 2008. "A sequential method for a class of pseudoconcave fractional problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 153-164, June.
    2. Hang-Chin Lai & Hui-Mei Chen, 2012. "Duality on a nondifferentiable minimax fractional programming," Journal of Global Optimization, Springer, vol. 54(2), pages 295-306, October.
    3. Jiawei Chen & Suliman Al-Homidan & Qamrul Hasan Ansari & Jun Li & Yibing Lv, 2021. "Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 221-243, April.

    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:137:y:2008:i:1:d:10.1007_s10957-007-9332-8. 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.