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Zbl 1065.90054
Cánovas, Lázaro; Cañavate, Roberto; Mar\'in, Alfredo
On the convergence of the Weiszfeld algorithm.
(English)
[J] Math. Program. 93, No. 2 (A), 327-330 (2002). ISSN 0025-5610; ISSN 1436-4646/e

The Weiszfeld algorithm is an iterative algorithm to solve the Fermat-Weber problem. {\it R. Chandrasekaran} and {\it A. Tamir} [Math. Program., Ser. A 44, No. 3, 293--295 (1989; Zbl 0683.90026)] stated the following conjecture: If the convex hull of the set of vertices is of full dimension, then the set of initial points for which the sequence generated by the Weiszfeld algorithm yields in a vertex is denumerable. {\it J. Brimberg} [Math. Program. 71, No. 1 (A), 71--76 (1995; Zbl 0855.90075)] claimed to prove the conjecture and extends it to a necessary and sufficient condition. The authors show in this paper that Brimberg's proof is not correct. Moreover, they show by examples that the conjecture cannot be extended to a necessary and sufficient condition.
[Stefan Nickel (Saarbrücken)]
MSC 2000:
*90B85 Continuous location
90C30 Nonlinear programming

Keywords: continuous location; Weiszfeld algorithm; convergence

Citations: Zbl 0683.90026; Zbl 0855.90075

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