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In a Hilbert setting, for convex differentiable optimization, we develop ageneral framework for adaptive accelerated gradient methods. They are based ondamped inertial dynamics where the coefficients are designed in a closed-loopway. Specifically, the damping is a feedback control of the velocity, or of thegradient of the objective function. For this, we develop a closed-loop versionof the time scaling and averaging technique introduced by the authors. We thusobtain autonomous inertial dynamics which involve vanishing viscous damping andimplicit Hessian driven damping. By simply using the convergence rates for thecontinuous steepest descent and Jensen's inequality, without the need forfurther Lyapunov analysis, we show that the trajectories have severalremarkable properties at once: they ensure fast convergence of values, fastconvergence of the gradients towards zero, and they converge to optimalsolutions. Our approach leads to parallel algorithmic results, that we study inthe case of proximal algorithms. These are among the very first general resultsof this type obtained using autonomous dynamics.

Fast convex optimization via closed-loop time scaling of gradient dynamics