On the Convergence of a Class of Iterative Methods for Solving the Weber Location Problem

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Abstract
The location problem is to find a point M whose sum of weighted distances from m vertices in p-dimensional Euclidean space is a minimum. The best-known algorithm for solving the location problem is an iterative scheme devised by Weiszfeld in 1937. The procedure will not converge if some nonoptimal vertex is an iterate, however. This paper solves the problem of vertex iterates and presents a general proof permitting a variable step length (within certain bounds). This property is used, in particular, to show the convergence of a modified gradient Newton-Raphson type of procedure.

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