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

This paper presents a procedure to solve the classical location median problem where the distances are measured with lp-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 lp norms and \({p \in (2, \infty)}\). The paper ends with a computational analysis of the different provided iterative schemes.