Approaching the solving of constrained variational inequalities via penalty term-based dynamical systems

摘要

We investigate the existence and uniqueness of (locally) absolutelycontinuous trajectories of a penalty term-based dynamical system associated toa constrained variational inequality expressed as a monotone inclusion problem.Relying on Lyapunov analysis and on the ergodic continuous version of thecelebrated Opial Lemma we prove weak ergodic convergence of the orbits to asolution of the constrained variational inequality under investigation. If oneof the operators involved satisfies stronger monotonicity properties, thenstrong convergence of the trajectories can be shown.