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Projected Dynamical Systems and Evolutionary Variational Inequalities via Hilbert Spaces with Applications1

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Abstract

In this paper, we make explicit the connection between projected dynamical systems on Hilbert spaces and evolutionary variational inequalities. We give a novel formulation that unifies the underlying constraint sets for such inequalities, which arise in time-dependent traffic network, spatial price equilibrium, and a variety of financial equilibrium problems. We emphasize the importance of the results in applications and provide a traffic network numerical example in which we compute the curve of equilibria.

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Author information

Authors and Affiliations

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

    M. G. Cojocaru (Assistant Professor)

  2. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    P. Daniele (Associate Professor)

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

    A. Nagurney (John F. Smith Memorial Professor)

Authors
  1. M. G. Cojocaru
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  2. P. Daniele
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  3. A. Nagurney
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Additional information

1This research was funded by the Rockefeller Foundation, Bellagio Center Program. The first author was also supported by NSERC Discovery Grant 045997 and the third author by NSF Grant IIS-0002647. The authors thank Professors George Isac, Antonino Maugeri, and Panos Pardalos for support and inspiration; they are indebted to Professor Antonino Maugeri for assistance throughout their residency at Bellagio, Italy in March 2004.

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Cojocaru, M.G., Daniele, P. & Nagurney, A. Projected Dynamical Systems and Evolutionary Variational Inequalities via Hilbert Spaces with Applications1 . J Optim Theory Appl 127, 549–563 (2005). https://doi.org/10.1007/s10957-005-7502-0

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