A subgradient procedure for the solution of minimax location problems

Abstract

Unconstrained planar minimax location problems are typically convex but not everywhere differentiable, thus precluding their solution by gradient techniques. We employ subgradients, which always exist, to the solution of some planar minimax location problems. A heuristic subgradient algorithm is presented for the solution of minimax location problems involving Euclidean and rectilinear distances. An attractive feature of the method is the ease of implementation on any size computer. We give a computational comparison of the algorithm with existing methods.