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: | Rosen J.B., Xue G.L. |
Keywords: | planning |
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.