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

M.G. Cojocaru, P. Daniele, A. Nagurney
Pareto Optimality, Game Theory and Equilibria, A. Chinchuluun – A. Migdalas – P.M. Pardalos – L. Pitsoulis Eds., Springer Optimization and its Applications, Springer, New York, 2008, 387-406.

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.

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