Minimax Theory and its Applications 04 (2019), No. 2, 355--386
Copyright Heldermann Verlag 2019
Multifacility Minimax Location Problems via Multi-Composed Optimization
Gert Wanka
Faculty of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany
gert.wanka@mathematik.tu-chemnitz.de
Oleg Wilfer
Faculty of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany
oleg.wilfer@mathematik.tu-chemnitz.de
We present a conjugate duality approach for multifacility minimax location problems with geometric constraints, where the underlying space is Banach 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.
Keywords: Conjugate duality, composed functions, minimax location problems, gauges, optimality conditions.
MSC: 49K35, 49N15, 90B85, 90C46, 90C47
[ Fulltext-pdf (288 KB)] for subscribers only.