On the structural monotone inclusion of continuous second-order dynamics combining dry friction and Hessian-driven damping

Abstract

To obtain the null point of the sum for a maximally monotone operator A and a cocoercive operator B, this article is concerned with the asymptotic properties of the trajectories to a second-order continuous damped autonomous dynamical systems with dry friction, which plays a crucial role for achieving stability within a finite time. Additionally, Hessian-driven damping is incorporated, which helps mitigating oscillations for inertial effects. The combination of dry friction and Hessian-driven damping in the context of split monotone inclusions represents a novel contribution, as it simultaneously ensures finite-time convergence and suppresses oscillatory behavior. The existence and uniqueness of global solutions, as well as the convergence of system trajectories are analyzed, the performance of the iterative algorithm generated by the second-order dynamic system discretely are also verified through several numerical experiments.