The Fermat-Torricelli Problem and Weiszfeld's Algorithm in the Light of Convex Analysis

2013/02/21 by Mordukhovich, Boris, Nam, Nguyen Mau · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1302.5244

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 \em 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 Rⁿ. 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.

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