Gert Wanka, Oleg Wilfer: Duality Results for Nonlinear Single Minimax Location Problems via Multi-Composed Optimization

Author(s):

Gert Wanka
Oleg Wilfer

Title:

Gert Wanka, Oleg Wilfer: Duality Results for Nonlinear Single Minimax Location Problems via Multi-Composed Optimization

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 02, 2016

Mathematics Subject Classification:

    none []

Abstract:

In the framework of conjugate duality we discuss nonlinear and linear single minimax location problems with geometric constraints, where the gauges are defined by convex sets of a Frechet space. The version of the nonlinear location problem is additionally considered with set-up costs. Associated dual problems for this kind of location problems will be formulated as well as corresponding duality statements. As conclusion of this paper, we give a geometrical interpretation of the optimal solutions of the dual problem of an unconstraint linear single minimax location problem when the gauges are a norm. For an illustration, an example in the Euclidean space will follow.

Keywords:

Conjugate Duality, Composed Functions, Gauges, Nonlinear Minimax Location Problems, Set-up Costs, Optimality Conditions

Language:

English

Publication time:

2/2016