An ordinary differential equation for modeling Halpern fixed-point algorithm

Abstract

The ordinary differential equation is a powerful tool for analyzing optimization algorithm. Motivated by the fact, this paper revisits Halpern fixed-point algorithm from an ordinary differential equation. More specifically, we establish a second-order ordinary differential equation with Hessian-driven damping, which is the limit of Halpern fixed-point algorithm. The Hessian-driven damping makes it possible to significantly attenuate the oscillations.