IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i2p587-603.html
   My bibliography  Save this article

Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions

Author

Listed:
  • M. Durea
  • R. Strugariu

Abstract

In this paper we give some calculus rules for tangent sets in the sense of Bouligand and Ursescu, as well as for corresponding derivatives of set-valued maps. Both first and second-order objects are envisaged and the assumptions we impose in order to get the calculus are in terms of metric subregularity of the assembly of the initial data. This approach is different from those used in alternative recent papers in literature and allows us to avoid compactness conditions. An application to a special type of vector optimization problems, where the objective is given as the sum of two multifunctions, is presented. Furthermore, also as application, a special attention is paid for the case of perturbation set-valued maps which naturally appear in optimization problems. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • M. Durea & R. Strugariu, 2013. "Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions," Journal of Global Optimization, Springer, vol. 56(2), pages 587-603, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:587-603
    DOI: 10.1007/s10898-011-9800-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-011-9800-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-011-9800-4?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. Marius Durea & Radu Strugariu, 2017. "Vectorial penalization for generalized functional constrained problems," Journal of Global Optimization, Springer, vol. 68(4), pages 899-923, August.
    2. Marius Durea & Diana Maxim & Radu Strugariu, 2021. "Metric Inequality Conditions on Sets and Consequences in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 744-771, June.
    3. Nguyen Minh Tung & Nguyen Xuan Duy Bao, 2022. "Higher-order set-valued Hadamard directional derivatives: calculus rules and sensitivity analysis of equilibrium problems and generalized equations," Journal of Global Optimization, Springer, vol. 83(2), pages 377-402, June.
    4. Teodor Chelmuş & Marius Durea & Elena-Andreea Florea, 2019. "Directional Pareto Efficiency: Concepts and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 336-365, July.
    5. Marius Durea & Radu Strugariu & Christiane Tammer, 2015. "On set-valued optimization problems with variable ordering structure," Journal of Global Optimization, Springer, vol. 61(4), pages 745-767, April.

    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:587-603. 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.