IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v171y2016i2d10.1007_s10957-016-0926-x.html
   My bibliography  Save this article

From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

Author

Listed:
  • Robert Baier

    (University of Bayreuth)

  • Elza Farkhi

    (Tel Aviv University)

  • Vera Roshchina

    (RMIT University)

Abstract

We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and a mean-value theorem. Thus, we extend the theory of the directed subdifferential from quasidifferentiable to directed subdifferentiable functions.

Suggested Citation

  • Robert Baier & Elza Farkhi & Vera Roshchina, 2016. "From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 384-401, November.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0926-x
    DOI: 10.1007/s10957-016-0926-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-016-0926-x
    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/s10957-016-0926-x?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.

    References listed on IDEAS

    as
    1. Y. Gao, 2004. "Representation of the Clarke Generalized Jacobian via the Quasidifferential," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 519-532, December.
    2. Robert Baier & Elza Farkhi & Vera Roshchina, 2010. "On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions," Springer Optimization and Its Applications, in: Regina S. Burachik & Jen-Chih Yao (ed.), Variational Analysis and Generalized Differentiation in Optimization and Control, pages 59-93, Springer.
    3. Robert Baier & Elza Farkhi & Vera Roshchina, 2014. "Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 391-414, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Alireza Kabgani, 2021. "Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 666-678, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Y. Gao, 2006. "Differences of Polyhedra in Matrix Space and Their Applications to Nonsmooth Analysis," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 431-442, September.
    2. Robert Baier & Elza Farkhi & Vera Roshchina, 2014. "Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 391-414, February.

    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:171:y:2016:i:2:d:10.1007_s10957-016-0926-x. 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.

    If CitEc recognized a bibliographic 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.

    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.