Duality results for nonlinear single minimax location problems via multi-composed optimization

Gert Wanka () and Oleg Wilfer ()
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Gert Wanka: Chemnitz University of Technology
Oleg Wilfer: Chemnitz University of Technology

Mathematical Methods of Operations Research, 2017, vol. 86, issue 2, No 8, 439 pages

Abstract: 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 Fréchet 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 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-017-0603-3

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