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On the global convergence of a generalized iterative procedure for the minisum location problem with ℓ p distances for p > 2

On the global convergence of a generalized iterative procedure for the minisum location problem... This paper presents a procedure to solve the classical location median problem where the distances are measured with ℓ p -norms with p > 2. In order to do that we consider an approximated problem. The global convergence of the sequence generated by this iterative scheme is proved. Therefore, this paper closes the still open question of giving a modification of the Weiszfeld algorithm that converges to an optimal solution of the median problem with ℓ p norms and $${p \in (2, \infty)}$$ . The paper ends with a computational analysis of the different provided iterative schemes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Programming Springer Journals

On the global convergence of a generalized iterative procedure for the minisum location problem with ℓ p distances for p > 2

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References (42)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer and Mathematical Optimization Society
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
ISSN
0025-5610
eISSN
1436-4646
DOI
10.1007/s10107-011-0501-z
Publisher site
See Article on Publisher Site

Abstract

This paper presents a procedure to solve the classical location median problem where the distances are measured with ℓ p -norms with p > 2. In order to do that we consider an approximated problem. The global convergence of the sequence generated by this iterative scheme is proved. Therefore, this paper closes the still open question of giving a modification of the Weiszfeld algorithm that converges to an optimal solution of the median problem with ℓ p norms and $${p \in (2, \infty)}$$ . The paper ends with a computational analysis of the different provided iterative schemes.

Journal

Mathematical Programming – Springer Journals

Published: Nov 11, 2011

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