# An inertial forward-backward algorithm for monotone inclusions

arXiv: https://arxiv.org/abs/1403.3522 · HTML: https://mlsanity.com/paper/1403.3522/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2014.

## Built on by (most cited first, 5 of 5)

- [Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions](https://mlsanity.com/paper/2110.08150/) (2021)
- [Accelerated nonlinear primal-dual hybrid gradient methods with applications to supervised machine learning](https://mlsanity.com/paper/2109.12222/) (2021)
- [Contractivity and linear convergence in bilinear saddle-point problems: An operator-theoretic approach](https://mlsanity.com/paper/2410.14592/) (2024)
- [A Double Inertial Forward-Backward Splitting Algorithm With Applications to Regression and Classification Problems](https://mlsanity.com/paper/2505.03794/) (2025)
- [Inertial Quadratic Majorization Minimization with Application to Kernel Regularized Learning](https://mlsanity.com/paper/2507.04247/) (2025)

## Abstract (arXiv)

In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method of Nesterov, but can be applied to a much larger class of problems including convex-concave saddle point problems and general monotone inclusions. We prove convergence of the algorithm in a Hilbert space setting and show that several recently proposed first-order methods can be obtained as special cases of the general algorithm. Numerical results show that the proposed algorithm converges faster than existing methods, while keeping the computational cost of each iteration basically unchanged.