# Inertial Three-Operator Splitting Method and Applications

## TL;DR

This paper presents an inertial three-operator splitting method for convex optimization, analyzing its convergence, providing adaptive parameter selection, and demonstrating its effectiveness in machine learning tasks.

## Contribution

It introduces an inertial variant of the forward-Douglas-Rachford splitting tailored for three-composite convex minimization, with convergence analysis and practical guidance.

## Key findings

- Convergence of the inertial method is established.
- The method performs well in machine learning applications.
- Adaptive inertial parameter selection improves practical performance.

## Abstract

We introduce an inertial variant of the forward-Douglas-Rachford splitting and analyze its convergence. We specify an instance of the proposed method to the three-composite convex minimization template. We provide practical guidance on the selection of the inertial parameter based on the adaptive starting idea. Finally, we illustrate the practical performance of our method in various machine learning applications.