Global Approximation of Solutions of Time-Dependent Variational Inequalities

Abstract

We consider a class of parametric variational inequalities where both the operator and the convex set depend on time. This kind of variational inequalities are useful to model many time dependent equilibrium problems. We study the Lipschitz continuity of the solutions with respect to the time parameter and construct approximations for them which minimize the average worst case error. Some improved estimates of the Lipschitz constant for this class of problems are given. In order to illustrate our procedure, we study a classical network equilibrium problem.

Keywords:

• Approximation
• Lipschitz continuity
• Monotonicity
• Time-dependent equilibrium problems
• Variational inequality
• Worst case error

Mathematics Subject Classification:

• 47J20
• 47H05

Acknowledgments

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