Skip to main content
SpringerLink
Log in

Linear convergence of generalized Weiszfeld's method

Lineare Konvergenz der verallgemeinerten Methode von Weiszfeld

  • Published:
Computing Aims and scope Submit manuscript

Abstract

Weiszfeld's method is widely used for solving problems of optimal location. It is shown that a very general variant of this method converges linearly thus generalizing a result of I. N. Katz.

Zusammenfassung

Zur Lösung von Standortoptimierungsproblemen wird häufig eine auf E. Weiszfeld zurückgehende Methode verwendet, von der I. N. Katz lokal lineare Konvergenz nachweisen konnte. Dieses Resultat wird in der vorliegenden Arbeit verallgemeinert.

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

Access this article

Log in via an institution

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. Bereanu, B.: Cu privire la problema amplasării optimale. In: Studii de statistică, Lucrările consfătuirii stiinţifice de statistică, 27–29 noiembrie 1961, pp. 103–113. Bucuresti: Direcţia centrală de statistică 1962.

    Google Scholar 

  2. Collatz, L., Wetterling, W.: Optimierungsaufgaben. (Heidelberger Taschenbücher, Band 15.) Berlin-Heidelberg-New York: Springer 1966. (2nd edition 1971.)

    Google Scholar 

  3. Daniel, J. W.: The approximate minimization of functionals. Englewood Cliffs, N. J.: Prentice-Hall, Inc. 1971.

    Google Scholar 

  4. Eckhardt, U.: On an optimization problem related to minimal surfaces with obstacles. In: Optimization and optimal control (Bulirsch, R., Oettli, W., Stoer, J., eds.) (Lecture Notes in Mathematics, Vol. 447), pp. 95–101. Berlin-Heidelberg-New York: Springer 1975.

    Google Scholar 

  5. Eckhardt, U.: On a minimization problem in structural mechanics. In: Optimization techniques, Part 2 (Stoer, J., ed.) (Lecture Notes in Control and Information Sciences, Vol. 7), pp. 42–50. Berlin-Heidelberg-New York: Springer 1978.

    Google Scholar 

  6. Eckhardt, U.: Weber's problem and Weiszfeld's algorithm in general spaces. Math. Programming18, 186–196 (1980).

    Google Scholar 

  7. Francis, R. L., White, J. A.: Facility layout and location: An analytical approach. Englewood Cliffs, N. J.: Prentice-Hall, Inc. 1974.

    Google Scholar 

  8. Katz, I. N.: Local convergence in Fermat's problem. Mathematical Programming6, 89–104 (1974).

    Google Scholar 

  9. Kuhn, H. W.: Locational problems and mathematical programming. In: Colloquium on applications of mathematics to economics (Prékopa, A., ed.), pp. 235–242. Budapest: Akadémiai Kiadó, Publishing House of the Hungarian Academy of Sciences 1965.

    Google Scholar 

  10. Mangasarian, O. L.: Nonlinear programming. New York etc.: McGraw-Hill 1969.

    Google Scholar 

  11. Weiszfeld, E.: Sur le point par lequel la somme des distances den points donnès est minimum. Tôhoku Mathematics J.43, 355–386 (1937).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich 6, Universität Essen, Universitätsstrasse 2, Postfach 68 43, D-4300, Essen 1, Federal Republic of Germany

    H. Voß

  2. Institut für Angewandte Mathematik, Universität Hamburg, Bundesstrasse 55, D-2000, Hamburg 13, Federal Republic of Germany

    U. Eckhardt

Authors
  1. H. Voß
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. U. Eckhardt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Prof. Dr. L. Collatz on the occasion of his 70th birthday, 6. July 1980.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voß, H., Eckhardt, U. Linear convergence of generalized Weiszfeld's method. Computing 25, 243–251 (1980). https://doi.org/10.1007/BF02242002

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02242002

Keywords

Search

Navigation