Multifacility Minimax Location Problems via Multi-Composed Optimization

We present a conjugate duality approach for multifacility minimax location problems with geometric constraints, where the underlying space is Fréchet and the distances are measured by gauges of closed convex sets. Besides assigning corresponding conjugate dual problems, we derive necessary and sufficient optimality conditions. Moreover, we introduce a further dual problem with less dual variables than the first formulated dual and deliver corresponding statements of strong duality and optimality conditions. To illustrate the results of the latter duality approach and to give a more detailed characterization of the relation between the location problem and its dual, we consider the situation in the Euclidean space.