ON THE CONVERGENCE OF A HYPERBOLOID APPROXIMATION PROCEDURE FOR THE PERTURBED EUCLIDEAN MULTIFACILITY LOCATION PROBLEM
成果类型：
Article
署名作者：
ROSEN, JB; XUE, GL
署名单位：
University of Vermont
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.41.6.1164
发表日期：
1993
页码：
1164-1171
关键词：
摘要：
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, we prove that the HAP is a descent algorithm and that it always converges to the minimizer of the objective function from any initial point.