# Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators

arXiv: https://arxiv.org/abs/1705.03803 · HTML: https://mlsanity.com/paper/1705.03803/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2017.

## Built on by (most cited first, 4 of 4)

- [Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developments](https://mlsanity.com/paper/2303.17192/) (2023)
- [Variance-Reduced Fast Krasnoselkii-Mann Methods for Finite-Sum Root-Finding Problems](https://mlsanity.com/paper/2406.02413/) (2024)
- [A Class of Accelerated Fixed-Point-Based Methods with Delayed Inexact Oracles and Its Applications](https://mlsanity.com/paper/2512.13547/) (2025)
- [Extragradient-Type Methods with O (1/k) Last-Iterate Convergence Rates for Co-Hypomonotone Inclusions](https://mlsanity.com/paper/2302.04099/) (2023)

## Abstract (arXiv)

We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying index, along with a new em Regularized Inertial Proximal Algorithm obtained by means of a convenient finite-difference discretization. These systems are the counterpart to accelerated forward-backward algorithms in the context of maximally monotone operators. A proper tuning of the parameters allows us to prove the weak convergence of the trajectories to zeroes of the operator. Moreover, it is possible to estimate the rate at which the speed and acceleration vanish. We also study the effect of perturbations or computational errors that leave the convergence properties unchanged. We also analyze a growth condition under which strong convergence can be guaranteed. A simple example shows the criticality of the assumptions on the Yosida approximation parameter, and allows us to illustrate the behavior of these systems compared with some of their close relatives.