IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-387-25570-5_5.html
   My bibliography  Save this book chapter

On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology

In: Essays and Surveys in Global Optimization

Author

Listed:
  • Hanif D. Sherali
  • Jitamitra Desai

Abstract

This paper provides an expository discussion on using the Reformulation-Linearization/Convexification (RLT) technique as a unifying approach for solving nonconvex polynomial, factorable, and certain black-box optimization problems. The principal RLT construct applies a Reformulation phase to add valid inequalities including polynomial and semidefinite cuts, and a Linearization phase to derive higher dimensional tight linear programming relaxations. These relaxations are embedded within a suitable branch-and-bound scheme that converges to a global optimum for polynomial or factorable programs, and results in a pseudo-global optimization method that derives approximate, near-optimal solutions for black-box optimization problems. We present the basic underlying theory, and illustrate the application of this theory to solve various problems.

Suggested Citation

  • Hanif D. Sherali & Jitamitra Desai, 2005. "On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology," Springer Books, in: Charles Audet & Pierre Hansen & Gilles Savard (ed.), Essays and Surveys in Global Optimization, chapter 0, pages 131-163, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25570-5_5
    DOI: 10.1007/0-387-25570-2_5
    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.

    Citations

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


    Cited by:

    1. M Laguna & J Molina & F Pérez & R Caballero & A G Hernández-Díaz, 2010. "The challenge of optimizing expensive black boxes: a scatter search/rough set theory approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 53-67, January.
    2. Teles, João P. & Castro, Pedro M. & Matos, Henrique A., 2013. "Univariate parameterization for global optimization of mixed-integer polynomial problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 613-625.
    3. Jitamitra Desai & Shalinee Kishore, 2017. "A global optimization framework for distributed antenna location in CDMA cellular networks," Annals of Operations Research, Springer, vol. 253(1), pages 169-191, June.

    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:978-0-387-25570-5_5. 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.