Revisiting several problems and algorithms in continuous location with ℓ_p norms [article]

Víctor Blanco, Justo Puerto, Safae El Haj Ben Ali
2013 arXiv   pre-print
This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different ℓ_p norms 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 ℓ_p ordered median location problems in dimension d (including of course the ℓ_p minisum or Fermat-Weber location problem for any p>
more » ... . We prove that this approach has a polynomial worse case complexity for monotone lambda weights and can be also applied to constrained and even non-convex problems.
arXiv:1312.7473v1 fatcat:6kftlishjbedxngz6vm6tjr7xa