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Minty variational inequalities and monotone trajectories of differential inclusions. (English) Zbl 1060.34029

Authors’ abstract: By P. Dupuis and A. Nagurney [Ann. Oper. Res. 44, No. 1–4, 9–42 (1993; Zbl 0785.93044)] the notion of “projected differential equation” has been introduced and the stability of solutions has been studied by means of Stampacchia type variational inequalities. More recently, in [(*) M. Pappalardo and M. Passacantando, J. Optimization Theory Appl. 113, No. 3, 567–582 (2002; Zbl 1017.49013)], Minty variational inequalities have been involved in the study of properties of the trajectories of such a projected differential equation.
We consider classical generalizations of both problems, namely projected differential inclusions and variational inequalities with point to set operators, and we extend results stated in (*) to this setting. Moreover, we also apply the results to describe the convergence of the trajectories of a generalized gradient inclusion method.

MSC:

34G25 Evolution inclusions
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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