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 language | English (US) |
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Pages (from-to) | 1164-1171 |
Number of pages | 8 |
Journal | Operations Research |
Volume | 41 |
Issue number | 6 |
DOIs | |
State | Published - 1993 |
Externally published | Yes |
ASJC Scopus subject areas
- Computer Science Applications
- Management Science and Operations Research