A Concise Lyapunov Analysis of Nesterov's Accelerated Gradient Method (2502.17373v2)

Abstract: Convergence analysis of Nesterov's accelerated gradient method has attracted significant attention over the past decades. While extensive work has explored its theoretical properties and elucidated the intuition behind its acceleration, a simple and direct proof of its convergence rates is still lacking. We provide a concise Lyapunov analysis of the convergence rates of Nesterov's accelerated gradient method for both general convex and strongly convex functions.