A globally convergent algorithm for facility location on a sphere

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper, we study the problem of facility location on a sphere. This is a generalization of the planar Euclidean facility location problem. This problem was first studied by Katz and Cooper and by Drezner and Wesolowsky where Weiszfeld-like algorithms were proposed. However, convergence has never been proved. In this paper, we first prove a hull property of the problem, i.e., every global minimizer is in the spherical convex hull of the existing facilities. We then study the relationship between the spherical facility location problem and a planar Euclidean facility location problem corresponding to each approximate solution to the spherical facility location problem. Optimality conditions for the spherical facility location problem are established in terms of optimality conditions for the corresponding planar Euclidean facility location problem and a gradient algorithm is proposed to solve the spherical facility location problem. We prove that our algorithm always converges to a global minimizer of the spherical facility location problem. Computational results are also given.

Original languageEnglish (US)
Pages (from-to)37-50
Number of pages14
JournalComputers and Mathematics with Applications
Volume27
Issue number6
DOIs
StatePublished - 1994
Externally publishedYes

Fingerprint

Facility Location
Facility Location Problem
Euclidean
Global Minimizer
Optimality Conditions
Gradient Algorithm
Convex Hull
Computational Results
Approximate Solution
Converge

Keywords

  • Global convergence
  • Gradient algorithms
  • Iterative algorithms without line search
  • Open problems
  • Optimality conditions
  • Spherical facility location

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

A globally convergent algorithm for facility location on a sphere. / Xue, Guoliang.

In: Computers and Mathematics with Applications, Vol. 27, No. 6, 1994, p. 37-50.

Research output: Contribution to journalArticle

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