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

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, thi...

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Bibliographic Details
Published in:Mathematical programming 2013, Vol.137 (1-2), p.477-502
Main Authors: Rodríguez-Chía, A. M., Valero-Franco, C.
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
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Summary: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 . The paper ends with a computational analysis of the different provided iterative schemes.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-011-0501-z