Degenerate Time-dependent Variational Inequalities with Applications to Traffic Equilibrium Problems

Projected Dynamical Systems and Evolutionary (time-dependent) Variational Inequalities via Hilbert Spaces with Applications

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, and a variety of financial equilibrium problems. We emphasize the importance of the results in ap...

Continuity results for a class of variational inequalities with applications to time dependent network problems

We consider a class of monotone variational inequalities in which both the operator and the convex set are parametrized by continuous functions. Under suitable assumptions, we prove the continuity of the solution with respect to the parameter. As an important application, we consider the case of finite dimensional variational inequalities on suitable polyhedra. We demonstrate the applicability ...

Regularity Results for Time-dependent Variational and Quasi-variational Inequalities with Applications to Dynamic Traffic Networks

The aim of this paper is to consider time-dependent variational and quasi-variational inequalities and to study under which assumptions the continuity of solutions with respect to the time can be ensured. Making on appropriate use of the set convergence in Mosco’s sense, we get the desiderate continuity results for strongly monotone variational and quasi-variational inequalities. The continuity...

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

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, and a variety of financial equilibrium problems. We emphasize the importance of the results in a...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points