A note on convergence in the single facility minisum location problem

A note on convergence in the single facility minisum location problem

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Article ID: iaor199982
Country: United Kingdom
Volume: 35
Issue: 9
Start Page Number: 25
End Page Number: 31
Publication Date: Apr 1998
Journal: Computers & Mathematics with Applications
Authors: ,
Keywords: graphs, networks
Abstract:

The single facility minisum location problem requires finding a point in RN that minimizes a sum of weighted distances to m given points. The distance measure is typically assumed in the literature to be either Euclidean or rectangular, or the more general lp norm. Global convergence 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 lp norm. An important outcome of this analysis is that the set of bad starting points will always have a measure zero in the solution space (RN), thereby validating the global convergence properties of the Weiszfeld procedure for any lp norm, p ∈ [1,2].

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