Fast Convergent Inertial Proximal Gradient Algorithms With Dry Friction for Nonconvex Optimization

Abstract

This letter investigates fast first-order methods for nonconvex optimization, inspired by a second-order dynamical system with vanishing damping and strongly convex dry friction. By discretizing this system, we propose a strongly convex dry-friction inertial proximal gradient algorithm, and establish its convergence and geometric convergence rate, under mild conditions. Moreover, an accelerated variant, which combines Nesterov’s accelerated gradient method with the strongly convex dry-friction inertial proximal gradient method, is introduced. Numerical experiments are reported to demonstrate the effectiveness of the proposed algorithms.