Accelerating convergence in minisum location problem with ℓp norms

This paper presents a procedure for accelerating convergence of the Weiszfeld algorithm in the classical single facility location median problem in which the distances are measured by ℓp-norms. To this end, we combined Steffensen's method, a generic acceleration scheme applied to iterative processes for solving fixed point equations, with the acceleration methods based on the transformation of the Weiszfeld algorithm by a factor which is a function of the parameter p. The convergence of the proposed methodology and the conditions under which it is guaranteed are analyzed. The computational results show that the total number of iterations to meet a given stopping criterion will be reduced with respect to the results obtained in other algorithms proposed in the literature. The running times are either reduced or quite similar with respect to the existing algorithms for which no results of convergence are provided.