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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Gert Wanka & Oleg Wilfer

Authors
  1. Gert Wanka
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  2. Oleg Wilfer
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Correspondence to Gert Wanka.

Additional information

This work was supported by the DFG (the German Research Foundation) under ProjectWA922/8-1.

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Wanka, G., Wilfer, O. Duality results for nonlinear single minimax location problems via multi-composed optimization. Math Meth Oper Res 86, 401–439 (2017). https://doi.org/10.1007/s00186-017-0603-3

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  • DOI: https://doi.org/10.1007/s00186-017-0603-3

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