GLOBAL CONVERGENCE OF A GENERALIZED ITERATIVE PROCEDURE FOR THE MINISUM LOCATION PROBLEM WITH L(P) DISTANCES

This paper considers a general form of the single facility minisum loc ation problem (also referred to as the Fermat-Weber problem), where di stances are measured by an I,norm. An iterative solution algorithm is given which generalizes the well-known Weiszfeld procedure for Euclide an distances. Global convergence of the algorithm is proven for any va lue of the parameter p in the closed interval [1, 2], provided an iter ate does not coincide with a singular point of the iteration functions . However, for p > 2, the descent property of the algorithm and as a r esult, global convergence, are no longer guaranteed. These results gen eralize the work of Kuhn for Euclidean (p = 2) distances.