A new algorithm for the minimax location problem with the closest distance

Abstract

This paper focuses on the constrained minimax location problem with the closest distance. Some properties concerning the existence and uniqueness of the optimal solution are provided. To achieve these results, we apply non-smooth approach that allow us to give the explicit solution structure of the constrained problem. Moreover, we develop an effective algorithm for solving this class of problems and we provide its convergence under some mild assumptions. At the end, some computational test problems are provided to illustrate the effectiveness of the method and certify the theoretical results. © 2022 Informa UK Limited, trading as Taylor & Francis Group.