A Dynamical Systems Perspective on Nesterov Acceleration

This article presents a dynamic system model describing Nesterov's accelerated gradient method. In contrast to earlier work, the derivation does not rely on a vanishing step size argument. It is shown that Nesterov's accelerated gradient method follows from discretizing an ordinary differential equation with a semi-implicit Euler integration scheme. We analyze both the corresponding differential equation as well as the discretization for obtaining insights into the phenomenon of acceleration. The analysis suggests that a curvature-dependent damping term lies at the heart of acceleration. We further establish connections between the discretized and the continuous-time dynamics.