A note on convergence in the single facility minisum location problem

J. Brimberg, R. Chen

Research output: Contribution to journalArticlepeer-review

Abstract

The single facility minisum location problem requires finding a point in ℛN that minimizes a sum of weighted distances to m given points. The distance measure is typically assumed in the literature to be either Euclidean or rectangular, or the more general lp norm. Global convergence of a well-known iterative solution method named the Weiszfeld procedure has been proven under the proviso that none of the iterates coincide with a singular point of the iteration functions. The purpose of this paper is to examine the corresponding set of "bad" starting points which result in failure of the algorithm for a general lp norm. An important outcome of this analysis is that the set of bad starting points will always have a measure zero in the solution space (ℛN), thereby validating the global convergence properties of the Weiszfeld procedure for any lp norm, p ∈ [1,2].

Original languageEnglish
Pages (from-to)25-31
Number of pages7
JournalComputers and Mathematics with Applications
Volume35
Issue number9
DOIs
StatePublished - May 1998

Keywords

  • Convergence
  • L norm
  • Single facility minisum location problem
  • Singular points

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