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: | Wanka Gert, Bo Radu Ioan, Vargyas Emese |
Keywords: | programming: convex |
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.