IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-981-10-8866-7_7.html
   My bibliography  Save this book chapter

Variational Methods and Optimization

In: An Introduction to Nonlinear Analysis and Fixed Point Theory

Author

Listed:
  • Hemant Kumar Pathak

    (Pandit Ravishankar Shukla University, School of Studies in Mathematics)

Abstract

The purpose of this chapter is to give an introduction of variational methods and optimization theory in a rather convincing manner along with results of nonlinear analysis leading to an applied environment. So, we have chosen variational principles as the starting point of our discussion in the framework of Banach space theory that leads to optimization with the observation that by applying the techniques involved in variational methods and optimization one can deal with some real-world problems that arise in nonlinear analysis. We initiate our discussion by presenting some variational principles and their applications. The epicenter of our discussion is the so-called Ekeland variational principle (in short, EVP). Indeed, we show that EVP is equivalent to some other well-known results of nonlinear analysis, notably Takahashi’s minimization theorem.

Suggested Citation

  • Hemant Kumar Pathak, 2018. "Variational Methods and Optimization," Springer Books, in: An Introduction to Nonlinear Analysis and Fixed Point Theory, chapter 0, pages 513-606, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-8866-7_7
    DOI: 10.1007/978-981-10-8866-7_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
    for a similarly titled item that would be available.

    More about this item

    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:spr:sprchp:978-981-10-8866-7_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.