IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-0-387-34221-4_9.html
   My bibliography  Save this book chapter

Complementarity constraints as nonlinear equations: Theory and numerical experience

In: Optimization with Multivalued Mappings

Author

Listed:
  • Sven Leyffer

    (Argonne National Laboratory)

Abstract

Summary Recently, it has been shown that mathematical programs with complementarity constraints (MPCCs) can be solved efficiently and reliably as nonlinear programs. This paper examines various nonlinear formulations of the complementarity constraints. Several nonlinear complementarity functions are considered for use in MPCC. Unlike standard smoothing techniques, however, the reformulations do not require the control of a smoothing parameter. Thus they have the advantage that the smoothing is exact in the sense that Karush-Kuhn-Tucker points of the reformulation correspond to strongly stationary points of the MPCC. A new exact smoothing of the well-known min function is also introduced and shown to possess desirable theoretical properties. It is shown how the new formulations can be integrated into a sequential quadratic programming solver, and their practical performance is compared on a range of test problems.

Suggested Citation

  • Sven Leyffer, 2006. "Complementarity constraints as nonlinear equations: Theory and numerical experience," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 169-208, Springer.
  • Handle: RePEc:spr:spochp:978-0-387-34221-4_9
    DOI: 10.1007/0-387-34221-4_9
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Sven Leyffer, 2009. "A Complementarity Constraint Formulation of Convex Multiobjective Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 257-267, May.
    2. Patrick Mehlitz, 2020. "A comparison of solution approaches for the numerical treatment of or-constrained optimization problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 233-275, May.
    3. Jacquet, Quentin & van Ackooij, Wim & Alasseur, Clémence & Gaubert, Stéphane, 2024. "Quadratic regularization of bilevel pricing problems and application to electricity retail markets," European Journal of Operational Research, Elsevier, vol. 313(3), pages 841-857.

    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:spochp:978-0-387-34221-4_9. 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.