An Extension of the Fermat-Torricelli Problem

Abstract

The Fermat-Torricelli problem is an optimization problem associated with a finite subset \(\{a_{j}\}_{j=1}^{q}\) of ℝN and a family \(\{c_{j}\}_{j=1}^{q}\) of positive weights. The function F to be minimized is defined by \(F(x)=\sum _{j=1}^{q}c_{j}\Vert x-a_{j}\Vert\). In this paper, we extend this problem to the case of volumes.