IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v50y2025i3p1654-1680.html
   My bibliography  Save this article

Optimality Conditions in Control Problems with Random State Constraints in Probabilistic or Almost Sure Form

Author

Listed:
  • Caroline Geiersbach

    (Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany)

  • René Henrion

    (Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany)

Abstract

In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. Although the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian random vectors in order to formulate fully explicit optimality conditions involving a spherical integral. In the almost sure case, we derive optimality conditions and compare them with a model based on robust constraints with respect to the (compact) support of the given distribution.

Suggested Citation

  • Caroline Geiersbach & René Henrion, 2025. "Optimality Conditions in Control Problems with Random State Constraints in Probabilistic or Almost Sure Form," Mathematics of Operations Research, INFORMS, vol. 50(3), pages 1654-1680, August.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:3:p:1654-1680
    DOI: 10.1287/moor.2023.0177
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2023.0177
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2023.0177?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
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    Statistics

    Access and download statistics

    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:inm:ormoor:v:50:y:2025:i:3:p:1654-1680. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.