# A Double Inertial Forward-Backward Splitting Algorithm With Applications to Regression and Classification Problems

arXiv: https://arxiv.org/abs/2505.03794 · HTML: https://mlsanity.com/paper/2505.03794/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 1 May 2025.

## Builds on (most cited first, 5 of 5)

- [Trajectory of Alternating Direction Method of Multipliers and Adaptive Acceleration](https://mlsanity.com/paper/1906.10114/) (2019)
- [An inertial forward-backward algorithm for monotone inclusions](https://mlsanity.com/paper/1403.3522/) (2014)
- [Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces](https://mlsanity.com/paper/1609.01627/) (2016)
- [Geometry of First-Order Methods and Adaptive Acceleration](https://mlsanity.com/paper/2003.03910/) (2020)
- [Convergence Results of Two-Step Inertial Proximal Point Algorithm](https://mlsanity.com/paper/2207.09668/) (2022)

## Abstract (arXiv)

This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under standard assumptions, our proposed algorithm demonstrates weak convergence. We present numerous experimental results to demonstrate the behavior of the developed algorithm by comparing it with existing algorithms in the literature for regression and data classification problems. Furthermore, these implementations suggest our proposed algorithm yields superior outcomes when benchmarked against other relevant algorithms in existing literature.