Mathematical Programming

, Volume 44, Issue 1, pp 293–295

Open questions concerning Weiszfeld's algorithm for the Fermat-Weber location problem

  • R. Chandrasekaran
  • A. Tamir

DOI: 10.1007/BF01587094

Cite this article as:
Chandrasekaran, R. & Tamir, A. Mathematical Programming (1989) 44: 293. doi:10.1007/BF01587094


The Fermat—Weber location problem is to find a point in ℝn that minimizes the sum of the weighted Euclidean distances fromm given points in ℝn. A popular iterative solution method for this problem was first introduced by Weiszfeld in 1937. In 1973 Kuhn claimed that if them given points are not collinear then for all but a denumerable number of starting points the sequence of iterates generated by Weiszfeld's scheme converges to the unique optimal solution. We demonstrate that Kuhn's convergence theorem is not always correct. We then conjecture that if this algorithm is initiated at the affine subspace spanned by them given points, the convergence is ensured for all but a denumerable number of starting points.

Key words

Location theoryThe Fermat—Weber location problemWeiszfeld's iterative algorithm

Copyright information

© The Mathematical Programming Society, Inc. 1989

Authors and Affiliations

  • R. Chandrasekaran
    • 1
  • A. Tamir
    • 2
    • 3
  1. 1.University of TexasDallasUSA
  2. 2.New York UniversityNew YorkUSA
  3. 3.Tel Aviv UniversityTel AvivIsrael