IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v160y2014i1d10.1007_s10957-013-0371-z.html
   My bibliography  Save this article

Calmness of the Argmin Mapping in Linear Semi-Infinite Optimization

Author

Listed:
  • M. J. Cánovas

    (Miguel Hernández University of Elche)

  • A. Hantoute

    (Universidad de Chile)

  • J. Parra

    (Miguel Hernández University of Elche)

  • F. J. Toledo

    (Miguel Hernández University of Elche)

Abstract

This paper characterizes the calmness property of the argmin mapping in the framework of linear semi-infinite optimization problems under canonical perturbations; i.e., continuous perturbations of the right-hand side of the constraints (inequalities) together with perturbations of the objective function coefficient vector. This characterization is new for semi-infinite problems without requiring uniqueness of minimizers. For ordinary (finitely constrained) linear programs, the calmness of the argmin mapping always holds, since its graph is piecewise polyhedral (as a consequence of a classical result by Robinson). Moreover, the so-called isolated calmness (corresponding to the case of unique optimal solution for the nominal problem) has been previously characterized. As a key tool in this paper, we appeal to a certain supremum function associated with our nominal problem, not involving problems in a neighborhood, which is related to (sub)level sets. The main result establishes that, under Slater constraint qualification, perturbations of the objective function are negligible when characterizing the calmness of the argmin mapping. This result also states that the calmness of the argmin mapping is equivalent to the calmness of the level set mapping.

Suggested Citation

  • M. J. Cánovas & A. Hantoute & J. Parra & F. J. Toledo, 2014. "Calmness of the Argmin Mapping in Linear Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 111-126, January.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:1:d:10.1007_s10957-013-0371-z
    DOI: 10.1007/s10957-013-0371-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0371-z
    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/s10957-013-0371-z?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.

    Citations

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


    Cited by:

    1. Diethard Klatte & Bernd Kummer, 2015. "On Calmness of the Argmin Mapping in Parametric Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 708-719, June.
    2. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.

    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:160:y:2014:i:1:d:10.1007_s10957-013-0371-z. 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.