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Optimization of functions by quasi-random search methods

Optimisierung von Funktionen durch quasi-zufällige Suchmethoden

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Abstract

It is shown how to effectively implement a deterministic analog of a Monte Carlo method for approximating the extreme values of a function. Numerical examples in a four-dimensional setting illustrate the usefulness of the method.

Zusammenfassung

Es wird gezeigt, wie man ein deterministisches Analogon einer Monte-Carlo-Methode zur Annäherung der Extremwerte einer Funktion zielführend zur Anwendung bringt. Numerische Beispiele für den vierdimensionalen Fall illustrieren die praktische Nützlichkeit der Methode.

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References

  1. Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. New York: Wiley- Interscience 1974.

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  2. Niederreiter, H.: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc. (to appear Nov. 1978).

  3. Niederreiter, H.: A quasi-Monte Carlo method for the approximate computation of the extreme values of a function. Paul Turán Memorial Volume (to appear).

  4. Zieliński, R.: On the Monte Carlo evaluation of the extremal value of a function. Algorytmy2, no. 4, 7–13 (1965).

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Authors and Affiliations

  1. Chair in Pure Mathematics, University of the West Indies, Kingston 7, Jamaica

    H. Niederreiter

  2. Department of Mathematics, University of Illinois, 61801, Urbana, IL, USA

    K. McCurley

Authors
  1. H. Niederreiter
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  2. K. McCurley
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Niederreiter, H., McCurley, K. Optimization of functions by quasi-random search methods. Computing 22, 119–123 (1979). https://doi.org/10.1007/BF02253124

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  • DOI: https://doi.org/10.1007/BF02253124

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