Nothing Special   »   [go: up one dir, main page]
Skip to main content
SpringerLink
Log in

A Multidimensional Branch-and-Prune Method for Interval Global Optimization

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

In this paper a new multidimensional extension of the recently developed one-dimensional enclosure method called kite is given for interval global optimization. A more sophisticated version of the pruning technique based on the kite method is introduced. By the new componentwise approach all the one-dimensional theoretical results and procedures can be used in the higher-dimensional case. The possibilities in the implementation of the new algorithm together with numerical results on 40 standard test problems are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Csendes and D. Ratz, Subdivision direction selection in interval methods for global optimization, SIAM J. Numer. Anal. 34(3) (1997) 922–938.

    Google Scholar 

  2. R. Hammer, M. Hocks, U. Kulisch and D. Ratz, C ++ Toolbox for Verified Computing I: Basic Numerical Problems: Theory, Algorithms, and Programs (Springer, Berlin, 1995).

    Google Scholar 

  3. E. Hansen, Global Optimization Using Interval Analysis (Marcel Decker, New York, 1992).

    Google Scholar 

  4. R.B. Kearfott, Rigorous Global Search: Continuous Problems (Kluwer, Boston, 1996).

    Google Scholar 

  5. F. Messine and J.-L. Lagouanelle, Enclosure methods for multivariate differentiable functions and application to global optimization, J. Universal Computer Sci. 4(6) (1998) 589–603.

    Google Scholar 

  6. R.E. Moore, Methods and Applications of Interval Analysis (SIAM, Philadelphia, PA, 1979).

    Google Scholar 

  7. A. Neumaier, Interval Methods for Systems of Equations (Cambridge Univ. Press, Cambridge, 1990).

    Google Scholar 

  8. H. Ratschek and J. Rokne, Computer Methods for the Range of Functions (Ellis Horwood, Chichester, 1984).

    Google Scholar 

  9. H. Ratschek and J. Rokne, New Computer Methods for Global Optimization (Ellis Horwood, Chichester, 1988).

    Google Scholar 

  10. D. Ratz, Automatische Ergebnisverifikation bei globalen Optimierungsproblemen, Ph.D. thesis, Universitaet Karlsruhe (1992).

  11. D. Ratz, Automatic Slope Computation and its Application in Nonsmooth Global Optimization (Shaker-Verlag, Aachen, 1998).

    Google Scholar 

  12. T. Vinkó, J.-L. Lagouanelle and T. Csendes, A new inclusion function for optimization: Kite–the one-dimensional case, J. Global Optimization (2004) in press.

Download references

Author information

Authors and Affiliations

  1. Research Group on Artificial Intelligence of the Hungarian Academy of Sciences, and, University of Szeged, H-6720, Szeged, Aradi vértanúk tere 1, Hungary

    Tamás Vinkó

  2. Department of Applied Informatics and Formal Descriptions, University of Karlsruhe, Karlsruhe, Germany

    Dietmar Ratz

Authors
  1. Tamás Vinkó
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dietmar Ratz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vinkó, T., Ratz, D. A Multidimensional Branch-and-Prune Method for Interval Global Optimization. Numerical Algorithms 37, 391–399 (2004). https://doi.org/10.1023/B:NUMA.0000049490.96077.99

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:NUMA.0000049490.96077.99

Search

Navigation