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Global Convergence of a Generalized Iterative Procedure for the Minisum Location Problem with lp Distances

Global Convergence of a Generalized Iterative Procedure for the Minisum Location Problem with lp... This paper considers a general form of the single facility minisum location problem (also referred to as the Fermat-Weber problem), where distances are measured by an lp norm. An iterative solution algorithm is given which generalizes the well-known Weiszfeld procedure for Euclidean distances. Global convergence of the algorithm is proven for any value of the parameter p in the closed interval [1, 2], provided an iterate does not coincide with a singular point of the iteration functions. However, for p > 2, the descent property of the algorithm and as a result, global convergence, are no longer guaranteed. These results generalize the work of Kuhn for Euclidean (p = 2) distances. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Operations Research INFORMS

Global Convergence of a Generalized Iterative Procedure for the Minisum Location Problem with lp Distances

Brimberg, Jack; Love, Robert F.
Operations Research , Volume 41 (6): 11 – Dec 1, 1993
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References (32)

Publisher
INFORMS
Copyright
Copyright © INFORMS
Subject
Research Article
ISSN
0030-364X
eISSN
1526-5463
DOI
10.1287/opre.41.6.1153
Publisher site
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Abstract

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

Journal

Operations Research – INFORMS

Published: Dec 1, 1993

Keywords: Keywords : facilities/equipment planning ; location ; continuous: convergence of a procedure for location with lp distances

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