Mathematical Programming

, Volume 4, Issue 1, pp 98–107 | Cite as

A note on Fermat's problem

  • Harold W. Kuhn
Article

Abstract

The General Fermat Problem asks for the minimum of the weighted sum of distances fromm points inn-space. Dozens of papers have been written on variants of this problem and most of them have merely reproduced known results. This note calls attention to the work of Weiszfeld in 1937, who may have been the first to propose an iterative algorithm. Although the same algorithm has been rediscovered at least three times, there seems to be no completely correct treatment of its properties in the literature. Such a treatment, including a proof of convergence, is the sole object of this note. Other aspects of the problem are given scant attention.

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References

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    L. Cooper, “Location-allocation problems,”Operations Research 11 (1963) 331–343.Google Scholar
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    H.W. Kuhn, “On a pair of dual nonlinear programs,” in:Methods of nonlinear programming, Ed. J. Abadie (North-Holland, Amsterdam, 1967) 38–54.Google Scholar
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    H.W. Kuhn and R.E. Kuenne, “An efficient algorithm for the numerical solution of the generalized Weber problem in spatial economics,”Journal of Regional Science 4 (1962) 21–33.Google Scholar
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    W. Miehle, “Link-length minimization in networks,”Operations Research 6 (1958) 232–243.Google Scholar
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    E. Weiszfeld, “Sur le point pour lequel la somme des distances den points donnés est minimum,”Tôhoku Mathematics Journal 43 (1937) 355–386.Google Scholar

Copyright information

© The Mathematical Programming Society 1973

Authors and Affiliations

  • Harold W. Kuhn
    • 1
  1. 1.Princeton UniversityPrincetonUSA

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