Mathematical Programming

, Volume 4, Issue 1, pp 98–107

A note on Fermat's problem

  • Harold W. Kuhn

DOI: 10.1007/BF01584648

Cite this article as:
Kuhn, H.W. Mathematical Programming (1973) 4: 98. doi:10.1007/BF01584648


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.

Copyright information

© The Mathematical Programming Society 1973

Authors and Affiliations

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

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