This paper considers the Fermat-Weber location problem. It is shown that, after a suitable initialization, the standard Newton method can be applied to the Fermat-Weber problem and is globally and locally quadratically convergent. A numerical comparison with the popular Weiszfeld algorithm shows that Newton’s method is significantly more efficient than the Weiszfeld scheme.

Fermat-Weber problem in its simple form (unconstrained, single facility, Euclidean metric) is well investigated. Lot of algorithms are also developed for more complicated cases. But the generalized multi-facility problem with barriers, restricted zones and an arbitrary metric has no well-known algorithm for its solving. In this paper, we consider the planar multi-facility Weber problem with res...