  We present a dynamical system framework for understanding Nesterov's
accelerated gradient method. In contrast to earlier work, our derivation does
not rely on a vanishing step size argument. We show that Nesterov acceleration
arises from discretizing an ordinary differential equation with a semi-implicit
Euler integration scheme. We analyze both the underlying differential equation
as well as the discretization to obtain insights into the phenomenon of
acceleration. The analysis suggests that a curvature-dependent damping term
lies at the heart of the phenomenon. We further establish connections between
the discretized and the continuous-time dynamics.
