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.

Keywords:

• Mosco convergence
• Multiclass network equilibrium problem
• Quasi-variational inequalities

Mathematics Subject Classification:

• Primary: 49J40, 90C33
• Secondary: 90B20

Acknowledgments

Part of the special issue, “Variational Analysis and Applications.”