On the convergence of the Weiszfeld algorithm
The Weiszfeld algorithm is an iterative algorithm to solve the Fermat-Weber problem. \textit{R. Chandrasekaran} and \textit{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. \textit{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.
scientific article; zbMATH DE number 1942743