Computational Aspects of the Fermat-Weber Problem and its Solution Algorithms

Abstract

This scientific article summarizes the most relevant computational aspects of the literature on the Fermat-Weber (FW) problem. The FW problem aims to compute a point that minimizes the sum of weighted Euclidean distances to $p$ fixed points in the plane. We present the pseudocodes, convergence analysis, computational implementation, and numerical simulations of all the methods explained in this scientific article. In the end, we give an example of image processing to determine the representative image of a set of images. All computational implementations are developed in MATLAB.