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

arXiv: https://arxiv.org/abs/1302.5244 · HTML: https://mlsanity.com/paper/1302.5244/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2013.

## Built on by (most cited first, 1 of 1)

- [Theory and Approximate Solvers for Branched Optimal Transport with Multiple Sources](https://mlsanity.com/paper/2210.07702/) (2022)

## Abstract (arXiv)

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.