The Fermat-Weber location problem is to find a point in ℝn that minimizes the sum of the weighted Euclidean distances from m given points in ℝn. A popular iterative solution method for this problem was first introduced by Weiszfeld in 1937. In 1973 Kuhn claimed that if the m given points are not collinear then for all but a denumerable number of starting points the sequence of iterates generated by Weiszfeld's scheme converges to the unique optimal solution. We demonstrate that Kuhn's convergence theorem is not always correct. We then conjecture that if this algorithm is initiated at the affine subspace spanned by the m given points, the convergence is ensured for all but a denumerable number of starting points.
- Location theory
- The Fermat-Weber location problem
- Weiszfeld's iterative algorithm