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Zbl 1176.90616
Weiszfeld, E.; Plastria, Frank
On the point for which the sum of the distances to $n$ given points is minimum. (English)
[J] Ann. Oper. Res. 167, 7-41 (2009). ISSN 0254-5330; ISSN 1572-9338/e

This article presents a translation in English of a 1937 French article by E. Weiszfeld. The article begins with the statement of the theorem that is to be proven, which determines the properties of the point for which the sum of the distances to $n$ given points is a minimum. After the statement of the theorem, the article presents three different proofs. The original terminology is used throughout this translation. The article concludes with an annex containing notes and comments by the translator.
[Efstratios Rappos (Athens)]

MSC 2000:: *90C35 Network programming
00B55 Miscellaneous volumes of translations
00B60 Collections of reprinted articles
90C90 Appl. of mathematical programming

Keywords: location problem; Weber problem; Euclidean distance; Weiszfeld algorithm

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