IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i2p691-711.html
   My bibliography  Save this article

Exactness and algorithm of an objective penalty function

Author

Listed:
  • Zhiqing Meng
  • Chuangyin Dang
  • Min Jiang
  • Xinsheng Xu
  • Rui Shen

Abstract

Penalty function is an important tool in solving many constrained optimization problems in areas such as industrial design and management. In this paper, we study exactness and algorithm of an objective penalty function for inequality constrained optimization. In terms of exactness, this objective penalty function is at least as good as traditional exact penalty functions. Especially, in the case of a global solution, the exactness of the proposed objective penalty function shows a significant advantage. The sufficient and necessary stability condition used to determine whether the objective penalty function is exact for a global solution is proved. Based on the objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions. Furthermore, the sufficient and necessary calmness condition on the exactness of the objective penalty function is proved for a local solution. An algorithm is presented in the paper in finding a local solution, with its convergence proved under some conditions. Finally, numerical experiments show that a satisfactory approximate optimal solution can be obtained by the proposed algorithm. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Zhiqing Meng & Chuangyin Dang & Min Jiang & Xinsheng Xu & Rui Shen, 2013. "Exactness and algorithm of an objective penalty function," Journal of Global Optimization, Springer, vol. 56(2), pages 691-711, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:691-711
    DOI: 10.1007/s10898-012-9900-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9900-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9900-9?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. Eric Rosenberg, 1981. "Globally Convergent Algorithms for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 437-444, August.
    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. Zhiqing Meng & Min Jiang & Rui Shen & Leiyan Xu & Chuangyin Dang, 2021. "An objective penalty function method for biconvex programming," Journal of Global Optimization, Springer, vol. 81(3), pages 599-620, November.

    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. Zhiqing Meng & Min Jiang & Rui Shen & Leiyan Xu & Chuangyin Dang, 2021. "An objective penalty function method for biconvex programming," Journal of Global Optimization, Springer, vol. 81(3), pages 599-620, November.

    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:jglopt:v:56:y:2013:i:2:p:691-711. 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.