In this paper we present some algorithms for solving a number of new models of facility location involving sets which generalize the classical Fermat-Torricelli problem. Our approach uses subgradient-type algorithms to cope with nondierentiabilty of the distance functions therein. Another approach involves approximating nonsmooth optimization problems by smooth optimizations problems using Nesterov's smoothing techniques. Convergence of the algorithms are proved. Extensive numerical results are also presented to show the effectiveness of the proposed algorithms.
View Nonsmooth Algorithms and Nesterov’s Smoothing Techniques for Generalized Fermat-Torricelli Problems