Abstract
In this paper we consider, in a general normed space, the optimization problem with the objective function being a composite of a convex and componentwise increasing function with a vector convex function. Perturbing the primal problem, we obtain, by means of the Fenchel-Rockafellar approach, a dual problem for it. The existence of strong duality is proved and the optimality conditions are derived.
Using this general result, we introduce the dual problem and the optimality conditions for the single facility location problem in a general normed space in which the existing facilities are represented by sets of points.
The classical Weber problem and minmax problem with demand sets are studied as particular cases of this problem.
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© 2003 Deutscher Universitäts-Verlag/GWV Fachverlage GmbH, Wiesbaden
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Boţ, R.I., Wanka, G. (2003). Duality for composed convex functions with applications in location theory. In: Habenicht, W., Scheubrein, B., Scheubrein, R. (eds) Multi-Criteria- und Fuzzy-Systeme in Theorie und Praxis. Deutscher Universitätsverlag. https://doi.org/10.1007/978-3-322-81539-2_1
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DOI: https://doi.org/10.1007/978-3-322-81539-2_1
Publisher Name: Deutscher Universitätsverlag
Print ISBN: 978-3-8244-7864-4
Online ISBN: 978-3-322-81539-2
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