Open questions concerning Weiszfeld's algorithm for the FermatWeber location problem
 R. Chandrasekaran,
 A. Tamir
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The Fermat—Weber location problem is to find a point in ℝ^{ n } that minimizes the sum of the weighted Euclidean distances fromm given points in ℝ^{ n }. 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.
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 Title
 Open questions concerning Weiszfeld's algorithm for the FermatWeber location problem
 Journal

Mathematical Programming
Volume 44, Issue 13 , pp 293295
 Cover Date
 19890501
 DOI
 10.1007/BF01587094
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Location theory
 The Fermat—Weber location problem
 Weiszfeld's iterative algorithm
 Industry Sectors
 Authors

 R. Chandrasekaran ^{(1)}
 A. Tamir ^{(2)} ^{(3)}
 Author Affiliations

 1. University of Texas, Dallas, TX, USA
 2. New York University, New York, NY, USA
 3. Tel Aviv University, Tel Aviv, Israel