A linear time algorithm for themini-max location problem

This paper considers the constrained mini-max locationproblem with the closest distance in the collinear case. Theexistence and uniqueness of the optimal solution areproved. In addition, we apply non-smooth approach thatallow us to give the explicit solution structure of theconstrained problem. Moreover, we develop an effectivealgorithm for solving this class of problems and we provideits convergence under some mild assumptions.

Keywords:

Global convergence , Location problem , Non-smoothoptimization , Mini-max