  The paper presents a new approach to solve multifacility location problems,
which is based on mixed integer programming and algorithms for minimizing
differences of convex (DC) functions. The main challenges for solving the
multifacility location problems under consideration come from their intrinsic
discrete, nonconvex, and nondifferentiable nature. We provide a reformulation
of these problems as those of continuous optimization and then develop a new DC
type algorithm for their solutions involving Nesterov's smoothing. The proposed
algorithm is computationally implemented via MATLAB numerical tests on both
artificial and real data sets.
