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General infinite dimensional duality and applications to evolutionary network equilibrium problems

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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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Authors and Affiliations

  1. Division of Engineering and Applied Science, Harvard University, Cambridge, MA, 02138, USA

    Patrizia Daniele

  2. Department of Mathematics and Computer Sciences, University of Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Patrizia Daniele

  3. D.I.M.E.T., Faculty of Engineering, University of Reggio Calabria, Località Feo di Vito, 89060, Reggio Calabria, Italy

    Sofia Giuffrè

Authors
  1. Patrizia Daniele
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  2. Sofia Giuffrè
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Correspondence to Patrizia Daniele.

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Daniele, P., Giuffrè, S. General infinite dimensional duality and applications to evolutionary network equilibrium problems. Optimization Letters 1, 227–243 (2007). https://doi.org/10.1007/s11590-006-0028-z

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  • DOI: https://doi.org/10.1007/s11590-006-0028-z

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