Duality for location problems with unbounded unit balls

Duality for location problems with unbounded unit balls

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Article ID: iaor2009137
Country: Netherlands
Volume: 179
Issue: 3
Start Page Number: 1252
End Page Number: 1265
Publication Date: Jun 2007
Journal: European Journal of Operational Research
Authors: , ,
Keywords: programming: convex
Abstract:

Given an optimization problem with a composite of a convex and componentwise increasing function with a convex vector function as objective function, by means of the conjugacy approach based on the perturbation theory, we determine a dual to it. Necessary and sufficient optimality conditions are derived using strong duality. Furthermore, as special case of this problem, we consider a location problem, where the ‘distances’ are measured by gauges of closed convex sets. We prove that the geometric characterization of the set of optimal solutions for this location problem given by Hinojosa and Puerto in a recently published paper can be obtained via the presented dual problem. Finally, the Weber and the minmax location problems with gauges are given as applications.

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