In this paper two algorithms based on the Weiszfeld method are proposed to solve the single facility continuous space location problem with distances modelled by some Lp-norm. The authors derive a generalization of the Weiszfeld method and prove its convergence for the Euclidean case (p=2) given some restrictions on the objective function related to quasiconvexity. They also show that the convergence property does not hold in general for other Lp-norms. Moreover, since the objective funtion is not everywhere differentiable, the authors use the well-known hyperbolic approximation to obtain an optimization problem which approximates uniformly the original one. An adapted version of the Weiszfeld method is then derived and its convergence is proved under some conditions for 1<p•2. Furthermore, it is also shown that both algorithms have a linear rate of convergence provided certain stronger conditions are satisfied. Finally, some computational results are presented.
