## Boris S. Mordukhovich, Nguyen Mau Nam, The Fermat-Torricelli problem and Weiszfeld’s algorithm in the light of convex analysis

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DOI: 10.23952/jano.1.2019.3.02
Volume 1, Issue 3, 31 December 2019, Pages 205-215

Abstract. In the early 17th century, Pierre de Fermat proposed the following problem: given three points in the plane, find a point such that the sum of its Euclidean distances to the three given points is minimal. This problem was solved by Evangelista Torricelli and was named the Fermat-Torricelli problem. A more general version of the Fermat-Torricelli problem asks for a point that minimizes the sum of the distances to a finite number of given points in $\Bbb R^n$. This is one of the main problems in location science. In this paper we revisit the Fermat-Torricelli problem from both theoretical and numerical viewpoints using some ingredients of convex analysis and optimization.