IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-94015-1_9.html
   My bibliography  Save this book chapter

Notes on Newton’s Method After 1960

In: Advances in Mathematics and Applications

Author

Listed:
  • José Mario Martínez

    (University of Campinas, Institute of Mathematics, Statistics and Scientific Computing)

Abstract

Some Newtonian ideas will be reported with respect to research areas that emerged in numerical Mathematics after, approximately, 1960. For the problems of solving nonlinear equations and unconstrained optimization, Quasi-Newton methods, which stayed in the mainstream of numerical optimization for more than 30 years, will be motivated and discussed. The topic of complexity in unconstrained optimization will be introduced and some fundamental results will be rigorously proved. Newtonian algorithmic schemes in Linear Programming, which emerged after 1984 and presently represent competitive alternatives for large-scale problems, will be commented. Finally, surprising negative results concerning the capacity of Newton’s method to detect approximate solutions of constrained optimization problems will be reported.

Suggested Citation

  • José Mario Martínez, 2018. "Notes on Newton’s Method After 1960," Springer Books, in: Carlile Lavor & Francisco A. M. Gomes (ed.), Advances in Mathematics and Applications, pages 203-218, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-94015-1_9
    DOI: 10.1007/978-3-319-94015-1_9
    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:978-3-319-94015-1_9. 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.