Analysis of continuous dynamical system models with Hessians derived from optimization methods

Abstract

A sequence of solutions generated by a continuous optimization method can be associated with a solution trajectory of the continuous dynamical system obtained by the continuous limit of step sizes being 0. Such dynamical systems can contain Hessians even when the original optimization methods do not. In this paper, we show the convergence rate of such dynamical systems via the method of Lyapunov functions and argue their optimality.