A generalized minisum location model in continuous space with distances measured by some Lp-norm is introduced. Using the well-known hyperbolic approximation, the paper derives for the perturbed problem an adapted version of the Weiszfeld method and proves its convergence for 1•p•2 under the assumption that the objective function satisfies a condition related to quasiconvexity. Moreover, applying a result by Voßi and Eckhardt it is shown that this method for a smaller class of functions converges linearly to the optimal solution. Finally, in the last section some computational results are presented.
