General infinite dimensional duality and applications to evolutionary network equilibrium problems |
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| Authors: | Patrizia Daniele Sofia Giuffrè |
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| Affiliation: | (1) Division of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA;(2) Department of Mathematics and Computer Sciences, University of Catania, Viale A. Doria, 6, 95125 Catania, Italy;(3) D.I.M.E.T., Faculty of Engineering, University of Reggio Calabria, Località Feo di Vito, 89060 Reggio Calabria, Italy |
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| Abstract: | In this paper the authors present an infinite dimensional duality theory for optimization problems and evolutionary variational inequalities where the constraint sets are given by inequalities and equalities. The difficulties arising from the structure of the constraint set are overcome by means of generalized constraint qualification assumptions based on the concept of quasi relative interior of a convex set. An application to a general evolutionary network model, which includes as special cases traffic, spatial price and financial equilibrium problems, concludes the paper. |
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