# Fast convergence of generalized forward-backward algorithms for structured monotone inclusions

arXiv: https://arxiv.org/abs/2107.10107 · HTML: https://mlsanity.com/paper/2107.10107/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2021.

## Built on by (most cited first, 6 of 6)

- [Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions](https://mlsanity.com/paper/2110.08150/) (2021)
- [Randomized Block-Coordinate Optimistic Gradient Algorithms for Root-Finding Problems](https://mlsanity.com/paper/2301.03113/) (2023)
- [Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developments](https://mlsanity.com/paper/2303.17192/) (2023)
- [An Inexact Halpern Iteration with Application to Distributionally Robust Optimization](https://mlsanity.com/paper/2402.06033/) (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)

In this paper, we develop rapidly convergent forward-backward algorithms for computing zeroes of the sum of finitely many maximally monotone operators. A modification of the classical forward-backward method for two general operators is first considered, by incorporating an inertial term (closed to the acceleration techniques introduced by Nesterov), a constant relaxation factor and a correction term. In a Hilbert space setting, we prove the weak convergence to equilibria of the iterates (xn), with worst-case rates of  o(n-2) in terms of both the discrete velocity and the fixed point residual, instead of the classical rates of cal O(n-1) established so far for related algorithms. Our procedure is then adapted to more general monotone inclusions and a fast primal-dual algorithm is proposed for solving convex-concave saddle point problems.