IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v54y2012i3p433-447.html
   My bibliography  Save this article

On saddle points in nonconvex semi-infinite programming

Author

Listed:
  • Francisco Guerra-Vázquez

    ()

  • Jan-J. Rückmann

    ()

  • Ralf Werner

    ()

Abstract

In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian fulfills saddle point optimality conditions, where for the first procedure both the original objective function and constraints (and for the second procedure only the constraints) are substituted by their pth powers with sufficiently large power p. These results allow that local duality theory and corresponding numerical methods (e.g. dual search) can be applied to a broader class of nonconvex problems. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Francisco Guerra-Vázquez & Jan-J. Rückmann & Ralf Werner, 2012. "On saddle points in nonconvex semi-infinite programming," Journal of Global Optimization, Springer, vol. 54(3), pages 433-447, November.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:433-447
    DOI: 10.1007/s10898-011-9753-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-011-9753-7
    Download Restriction: Access to full text is restricted to subscribers.

    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. Qingxiang Zhang, 2009. "Optimality conditions and duality for semi-infinite programming involving B-arcwise connected functions," Computational Optimization and Applications, Springer, vol. 45(4), pages 615-629, December.
    2. Nader Kanzi, 2011. "Necessary optimality conditions for nonsmooth semi-infinite programming problems," Journal of Global Optimization, Springer, vol. 49(4), pages 713-725, April.
    Full references (including those not matched with items on IDEAS)

    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:54:y:2012:i:3:p:433-447. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.