A NOTE ON CONVERGENCE IN THE SINGLE FACILITY MINISUM LOCATION PROBLEM

The single facility minisum location problem requires finding a point in R-N that minimizes a sum of weighted distances to m given points. T he distance measure is typically assumed in the literature to be eithe r Euclidean or rectangular, or the more general l(p) norm. Global conv ergence of a well-known iterative solution method named the Weiszfeld procedure has been proven under the proviso that none of the iterates coincide with a singular point of the iteration functions. The purpose of this paper is to examine the corresponding set of ''bad'' starting points which result in failure of the algorithm for a general l(p) no rm. An important outcome of this analysis is that the set of bad start ing points will always have a measure zero in the solution space (RN), thereby validating the global convergence properties of the Weiszfeld procedure for any l(p) norm, p is an element of [1, 2].