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Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ℓτ norms

V. Blanco,J. Puerto,S. E. Ben-Ali

Published 2013 in Computational optimization and applications

ABSTRACT

This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different $$\ell _\tau $$ℓτ norms, $$\tau \ge 1$$τ≥1, in the demand points. We analyze the difficulty of this family of problems and revisit convergence properties of some well-known algorithms. The ultimate goal is to provide a common approach to solve the family of continuous $$\ell _\tau $$ℓτ ordered median location problems Nickel and Puerto (Facility location: a unified approach, 2005) in dimension $$d$$d (including of course the $$\ell _\tau $$ℓτ minisum or Fermat-Weber location problem for any $$\tau \ge 1$$τ≥1). We prove that this approach has a polynomial worst case complexity for monotone lambda weights and can be also applied to constrained and even non-convex problems.

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