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Pareto Optimality, Game Theory And Equilibria pp 387–406Cite as

Projected Dynamical Systems, Evolutionary Variational Inequalities, Applications, and a Computational Procedure

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Part of the Springer Optimization and Its Applications book series (SOIA,volume 17)

In this paper, we establish the equivalence between the solutions to an evolutionary variational inequality and the critical points of a projected dynamical system in infinite-dimensional spaces. We then present an algorithm, with convergence results, for the computation of solutions to evolutionary variational inequalities based on a discretization method and with the aid of projected dynamical systems theory. A numerical traffic network example is given for illustrative purposes.

Keywords

  • projected dynamical systems
  • evolutionary variational inequalities
  • critical points
  • regularization procedure
  • discretization

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Guelph, Canada

    Monica–Gabriela Cojocaru

  2. Department of Mathematics and Statistics, University of Catania, Catania, Italy

    Patrizia Daniele

  3. Department of Finance and Operations Management, University of Massachusetts, Amherst, MA, USA

    Anna Nagurney

Authors
  1. Monica–Gabriela Cojocaru
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  2. Patrizia Daniele
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  3. Anna Nagurney
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Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos, Altannar Chinchuluun & Panos M. Pardalos,  & 

  2. Department of Production Engineering and Management, Technical University of Crete, 73100, Greece

    Athanasios Migdalas

  3. Department of Production Engineering and Management, Aristotle University of Thessaloniki, Greece

    Leonidas Pitsoulis

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Cojocaru, M., Daniele, P., Nagurney, A. (2008). Projected Dynamical Systems, Evolutionary Variational Inequalities, Applications, and a Computational Procedure. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds) Pareto Optimality, Game Theory And Equilibria. Springer Optimization and Its Applications, vol 17. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77247-9_14

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