IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v64y2016i2d10.1007_s10589-015-9817-6.html
   My bibliography  Save this article

A generalization of $$\omega $$ ω -subdivision ensuring convergence of the simplicial algorithm

Author

Listed:
  • Takahito Kuno

    (University of Tsukuba)

  • Tomohiro Ishihama

    (NS Solutions Corporation)

Abstract

In this paper, we refine the proof of convergence by Kuno–Buckland (J Global Optim 52:371–390, 2012) for the simplicial algorithm with $$\omega $$ ω -subdivision and generalize their $$\omega $$ ω -bisection rule to establish a class of subdivision rules, called $$\omega $$ ω -k-section, which bounds the number of subsimplices generated in a single execution of subdivision by a prescribed number k. We also report some numerical results of comparing the $$\omega $$ ω -k-section rule with the usual $$\omega $$ ω -subdivision rule.

Suggested Citation

  • Takahito Kuno & Tomohiro Ishihama, 2016. "A generalization of $$\omega $$ ω -subdivision ensuring convergence of the simplicial algorithm," Computational Optimization and Applications, Springer, vol. 64(2), pages 535-555, June.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:2:d:10.1007_s10589-015-9817-6
    DOI: 10.1007/s10589-015-9817-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-015-9817-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-015-9817-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. Locatelli & U. Raber, 2000. "Finiteness Result for the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 81-88, October.
    2. Nguyen Van Thoai & Hoang Tuy, 1980. "Convergent Algorithms for Minimizing a Concave Function," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 556-566, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Takahito Kuno, 2018. "A modified simplicial algorithm for convex maximization based on an extension of $$\omega $$ ω -subdivision," Journal of Global Optimization, Springer, vol. 71(2), pages 297-311, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. N. V. Thoai, 2000. "Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 331-354, November.
    2. Collet, J.H., 1983. "Use of temperature-green functions for calculations of second-order susceptibilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(1), pages 85-91.
    3. B. Jaumard & C. Meyer, 2001. "On the Convergence of Cone Splitting Algorithms with ω-Subdivisions," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 119-144, July.
    4. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    5. Takahito Kuno, 2018. "A modified simplicial algorithm for convex maximization based on an extension of $$\omega $$ ω -subdivision," Journal of Global Optimization, Springer, vol. 71(2), pages 297-311, June.
    6. Harold P. Benson, 1996. "Deterministic algorithms for constrained concave minimization: A unified critical survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 765-795, September.
    7. N. V. Thoai, 2010. "Reverse Convex Programming Approach in the Space of Extreme Criteria for Optimization over Efficient Sets," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 263-277, November.
    8. Takahito Kuno & Paul Buckland, 2012. "A convergent simplicial algorithm with ω-subdivision and ω-bisection strategies," Journal of Global Optimization, Springer, vol. 52(3), pages 371-390, March.
    9. N. V. Thoai & Y. Yamamoto & A. Yoshise, 2005. "Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 467-490, February.

    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:coopap:v:64:y:2016:i:2:d:10.1007_s10589-015-9817-6. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.