IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-67168-0_6.html
   My bibliography  Save this book chapter

The Effect of Hessian Evaluations in the Global Optimization αBB Method

In: Modeling, Simulation and Optimization of Complex Processes HPSC 2015

Author

Listed:
  • Milan Hladík

    (Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics)

Abstract

We consider convex underestimators that are used in the global optimization αBB method and its variants. The method is based on augmenting the original nonconvex function by a relaxation term that is derived from an interval enclosure of the Hessian matrix. In this paper, we discuss the advantages of symbolic computation of the Hessian matrix. Symbolic computation often allows simplifications of the resulting expressions, which in turn means less conservative underestimators. We show by examples that even a small manipulation with the symbolic expressions, which can be processed automatically by computers, can have a large effect on the quality of underestimators. The purpose of this paper is also to turn attention of researchers to the possibility of symbolic differentiation (and its combination with automatic differentiation) and investigation of the most convenient way for interval evaluation.

Suggested Citation

  • Milan Hladík, 2017. "The Effect of Hessian Evaluations in the Global Optimization αBB Method," Springer Books, in: Hans Georg Bock & Hoang Xuan Phu & Rolf Rannacher & Johannes P. Schlöder (ed.), Modeling, Simulation and Optimization of Complex Processes HPSC 2015, pages 67-79, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-67168-0_6
    DOI: 10.1007/978-3-319-67168-0_6
    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

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:978-3-319-67168-0_6. 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.