Asymptotic behavior of penalty dynamics for constrained variational inequalities

Abstract: We propose a comprehensive framework for solving constrained variational inequalities via various classes of evolution equations displaying multi-scale aspects. In a Hilbertian framework, the class of dynamical systems we propose combine Tikhonov regularization and exterior penalization terms in order to yield simultaneously strong convergence of trajectories to least norm solutions in the constrained domain. Our construction thus unifies the literature on regularization methods and penalty-term based dynamical systems.