Fast Proximal Methods via Time Scaling of Damped Inertial Dynamics

In a Hilbert space setting, we consider a class of inertial proximal algorithms for nonsmooth convex optimization, with fast convergence properties. They can be obtained by time discretization of inertial gradient dynamics which have been rescaled in time. We will rely specifically on the recent development linking Nesterov's accelerated method with vanishing damping inertial dynamics. Doing so, we obtain a dynamical interpretation of the seminal papers of Güler on the convergence rate of the proximal methods for convex optimization.