IDEAS home Printed from https://ideas.repec.org/h/spr/lnechp/978-3-642-04900-2_7.html
   My bibliography  Save this book chapter

Applications of the Duality to Monotone Operators

In: Conjugate Duality in Convex Optimization

Author

Listed:
  • Radu Ioan Boţ

    (Chemnitz University of Technology)

Abstract

The theory of monotone operators captured the attention of mathematicians not only because of the fineness of the results but also because of the large number of applications, especially in fields like nonlinear analysis, variational inequalities and partial differential equations (see for instance [88, 130]). Different attempts to establish links to the convex analysis have been made (see [90,91,119]), but the most fruitful ones turned out to be the ones based on the so-called Fitzpatrick function discovered by Simons Fitzpatrick in [70]. Neglected for many years until re-popularized in [7, 8, 52, 98, 104–106, 121], this class of functions along with its extensions have given rise to a great number of publications which rediscovered and extended the important results of the theory of monotone operators by using tools from the convex analysis. The investigations we make in this chapter are to be seen belonging to this class of results, whereby, we concentrate ourselves on results based on the conjugate duality theory.

Suggested Citation

  • Radu Ioan Boţ, 2010. "Applications of the Duality to Monotone Operators," Lecture Notes in Economics and Mathematical Systems, in: Conjugate Duality in Convex Optimization, chapter 0, pages 133-155, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-04900-2_7
    DOI: 10.1007/978-3-642-04900-2_7
    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.

    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:lnechp:978-3-642-04900-2_7. 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.