On the convergence of a Hyperboloid Approximation Procedure for the perturbed Euclidean multifacility location problem

On the convergence of a Hyperboloid Approximation Procedure for the perturbed Euclidean multifacility location problem

0.00 Avg rating0 Votes
Article ID: iaor199543
Country: United States
Volume: 41
Issue: 6
Start Page Number: 1164
End Page Number: 1171
Publication Date: Nov 1993
Journal: Operations Research
Authors: ,
Keywords: planning
Abstract:

For the Euclidean single facility location problem, E. Weiszfeld proposed a simple closed-form iterative algorithm in 1937. Later, numerous authors proved that it is a convergent descent algorithm. In 1973, J. Eyster, J. White and W. Wierwille extended Weiszfeld’s idea and proposed a Hyperboloid Approximation Procedure (HAP) for solving the Euclidean multifacility location problem. They believed, based on considerable computational experience, that the HAP always converges. In 1977, Ostresh proved that the HAP is a descent algorithm under certain conditions. In 1981, Morris proved that a variant of the HAP always converges. However, no convergence proof for the original HAP has ever been given. In this paper, the authors prove that the HAP is a descent algorithm and that it always converges to the minimizer of the objective function from any initial point.

Reviews

Required fields are marked *. Your email address will not be published.