Evolutionary Quasi-Variational Inequalities and the Dynamic Multiclass Network Equilibrium Problem

Abstract

We give an existence result to a class of evolutionary quasi-variational inequalities with adaptive set of feasible solutions, where the adaptivity is modeled by solution-dependent equality constraints. A fundamental role will be played by the concept of Mosco convergence related to set-valued applications. Finally, we apply our achievements to the dynamic multiclass network equilibrium problem and provide a numerical example.

The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints

“…In order to prove Theorem 2.1, let us recall some definitions and a general existence result (see [18,31]). …”

Inverse problems for quasi-variational inequalities

“…The theory of quasi-variational inequalities has now established itself as one of the most promising areas of applied mathematics, offering a powerful mathematical apparatus for investigating a broad range of problems arising in diverse disciplines. Applications of quasivariational inequalities can be found in material science [12], equilibrium models [2,22], financial models [6], frictional elastostatic contact [19], image processing [16], sand-piles formation [3], and numerous others.…”