A Speed Restart Scheme for a Dynamical System with Hessian-Driven Damping and Three Constant Coefficients

TL;DR

This paper introduces a speed restart scheme for a Hessian-driven damped inertial system, achieving linear convergence without strong convexity assumptions, and demonstrates improved convergence in both continuous and discrete algorithms.

Contribution

The paper proposes a novel speed restart scheme for Hessian-driven damping systems that guarantees linear convergence without requiring strong convexity.

Findings

Linear convergence rate established for the restarted system

Numerical experiments show improved convergence rates

Effective in both continuous dynamics and inertial algorithms

Abstract

In this paper, we study a speed restart scheme for an inertial system with Hessian-driven damping. We establish a linear convergence rate for the function values along the restarted trajectories without assuming the strong convexity of the objective function. Our numerical experiments show improvements in the convergence rates, both for the continuous-time dynamics, and when applied to inertial algorithms as a heuristic