Advertisement

Computing

, Volume 38, Issue 3, pp 275–280 | Cite as

An interval version of Shubert's iterative method for the localization of the global maximum

  • Z. Shen
  • Y. Zhu
Short Communications

Abstract

Using the “bisection rule” of Moore, a simple algorithm is given which is an interval version of Shubert's iterative method for seeking the global maximum of a function of a single variable defined on a closed interval [a, b]. The algorithm which is always convergent can be easily extended to the higher dimensional case. It seems much simpler than and produces results comparable to that proposed by Shubert and Basso.

AMS (MOS) Subject Classifications

65K05 90C30 

Key words

Interval analysis global maximum iterative method 

Ein Intervallversion der iterativen Methode von Shubert zur Lokalisierung des globalen Maximums

Zusammenfassung

Unter Verwendung der “Bisektionsregel” von Moore wird ein Algorithmus angegeben, der eine Intervallversion der iterativen Methode von Shubert zur Bestimmung des globalen Maximums einer Funktion einer Veränderlichen auf den abgeschlossenen Intervall [a, b] darstellt. Der Algorithmus konvergiert immer; er kann leicht auf den höherdimensionalen Fall ausgedehnt werden. Er erscheint viel einfacher als der Algorithmus von Shubert und Basso, ergibt aber vergleichbare Ergebnisse.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Asaithambi, N. S., Shen, Z., Moore, R. E.: On computing the range of values. Computing28, 225–237 (1982).Google Scholar
  2. [2]
    Basso, P: Iterative methods for the localization of the maximum. SIAM J. Number. Anal.19, 781–792 (1982).CrossRefGoogle Scholar
  3. [3]
    Hansen, E.: Global optimization using interval analysis — a the one-dimensional case. J. Optim. Theory Appl.29, 331–344 (1979).CrossRefGoogle Scholar
  4. [4]
    Hansen, E.: Global optimization using interval analysis — the multi-dimensional case. Numer. Math.34, 247–270 (1980).CrossRefGoogle Scholar
  5. [5]
    Moore, R. E.: Methods and applications of interval analysis. SIAM Philadelphia, 1979.Google Scholar
  6. [6]
    Ratschek, H.: Inclusion functions and global optimization. Mathematical Programming, to appear (1985).Google Scholar
  7. [7]
    Shubert, B. O.: A sequential method seeking the global maximum of a function. SIAM J. Number. Anal.9, 379–388 (1972).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Z. Shen
    • 1
  • Y. Zhu
    • 1
  1. 1.Department of MathematicsNanjing UniversityNanjingThe People's Republic of China

Personalised recommendations