Single facility minisum location on curves (Q2708490)

In the minisum (or Fermat-Weber) location problem there are given \(n\) distinct points in \(\mathbb{R}^2\). The goal is to find a point \(y\) in \(\mathbb{R}^2\) such that the sum of the Euclidean distances to the given \(n\) points is minimized. The classical solution algorithm by Weiszfeld is based on an iterative algorithm using the derivative of the objective function. In this paper the solution is required to lie on a prespecified curve. Weizfeld type solution procedures for the case of a line segment and a circle are given without any proof of convergence. NEWLINENEWLINENEWLINEThe paper is well structured but the relation to the existing literature is not very well worked out.