Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Interval-majorant method and global optimization

Eine Intervall-Majoranten-Methode zur globalen Optimierung

  • 28 Accesses

  • 2 Citations


For seeking the global maximum of a function of a single variable defined on a closed interval [a, b] an interval-majorant method is proposed. This method derives advantages and avoids defects from both the one-step strategy method and the interval method. Numerical results are given.


Zur Bestimmung des globalen Maximums einer Funktion einer Veränderlichen auf einem abgeschlossenen Intervall [a, b] schlagen wir eine Intervall-Majoranten-Methode vor. Sie benützt die Vorteile und vermeidet die Nachteile zweier bekannter Verfahren. Numerische Resultate werden berichtet.

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


  1. [1]

    Basso, P.: Iterative methods for the localization of the global maximum. SIAM J. Numer. Anal.19, 781–782 (1982).

  2. [2]

    Basso, P.: Optimal search for the global maximum of function with bounded seminorm. SIAM J. Numer. Anal.22, 888–903 (1985).

  3. [3]

    Korotchenko, A. G.: An algorithm for seeking the maximum value of univariate function. USSR Comput. Math. Math. Phys.18 34–35 (1978).

  4. [4]

    Kulisch, U.: FORTRAN-SC, FORTRAN for Scientific Computation. Inst. Appl. Math., Univ. Karlsruhe, 1988.

  5. [5]

    Moore, R. E.: On computing the range of a rational function ofn variables over a bounded region. Computing16, 1–15 (1976).

  6. [6]

    Moore, R. E.: Methods and Applications of Interval Analysis. Philadelphia: SIAM 1979.

  7. [7]

    Piyavskii, G. B.: An algorithm for finding the absolute extremum of a function. USSR Comput. Math. Math. Phys.12, 57–67 (1972).

  8. [8]

    Shen Zuhe, Zhu Yiran: An interval version of Shubert's iterative method for the localization of the global maximum. Computing38, 275–280 (1987).

  9. [9]

    Shubert, B. O.: A sequential method seeking the global maximum of a function. SIAM J. Numer. Anal.9, 379–388 (1972).

Download references

Author information

Additional information

This paper was written while the first author worked as a visiting professor at the Institut für Angewandte Mathematik of the University of Freiburg i. Br./West Germany. It has been sponsored by Stiftung Volkswagenwerk, number I/63 064.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zuhe, S., Eiermann, M.C. Interval-majorant method and global optimization. Computing 43, 85–92 (1989).

Download citation

AMS Subject Classifications

  • 65K10
  • 65G10

Key words

  • Global optimization
  • guaranteed error bounds
  • interval analysis