On the convergence of a hyperboloid approximation procedure for the perturbed euclidean multifacility location problem

J. B. Rosen, G. L. Xue

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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 Hyperbloid. 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.

Original languageEnglish (US)
Pages (from-to)1164-1171
Number of pages8
JournalOperations Research
Volume41
Issue number6
DOIs
StatePublished - Jan 1 1993
Externally publishedYes

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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