The Fermat-Torricelli Problem and Weiszfeld's Algorithm in the Light of Convex Analysis
Optimization and Control
2019-12-25 v4
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 . 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.
Keywords
Cite
@article{arxiv.1302.5244,
title = {The Fermat-Torricelli Problem and Weiszfeld's Algorithm in the Light of Convex Analysis},
author = {Boris Mordukhovich and Nguyen Mau Nam},
journal= {arXiv preprint arXiv:1302.5244},
year = {2019}
}