On the convergence of the generalized Weiszfeld algorithm

On the convergence of the generalized Weiszfeld algorithm

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Article ID: iaor200971079
Country: Germany
Volume: 167
Issue: 1
Start Page Number: 327
End Page Number: 336
Publication Date: Mar 2009
Journal: Annals of Operations Research
Authors:
Keywords: Weber problem
Abstract:

In this paper we consider Weber-like location problems. The objective function is a sum of terms, each a function of the Euclidean distance from a demand point. We prove that a Weiszfeld-like iterative procedure for the solution of such problems converges to a local minimum (or a saddle point) when three conditions are met. Many location problems can be solved by the generalized Weiszfeld algorithm. There are many problem instances for which convergence is observed empirically. The proof in this paper shows that many of these algorithms indeed converge.

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