Geometric aspects of the generalized Fermat-Torricelli problem

The (generalized) Fermat-Torricelli problem to the unique point x is an element of R-d having the minimal (weighted) distance sum to n non-collinear points in R-d. Together with various generalizations, this problem is interesting from the purely mathematical point of view as well as in several parts of applied mathematics (location science, robust statistics etc.). We shall give straightforward proofs of some theorems referring to this problem and a survey on geometric aspects of it, containing geometric constructability, multifocal ellipses, natural generalizations of the geometric configuration itself etc.; also we present some historical corrections which seem to be worth mentioning. Finally, a geometric generalization of the Vecten-Fasbender duality (which seems to be the oldest example of dualizing problems in the sense of nonlinear programming) is given.