# Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms

## TL;DR

This paper introduces new inexact, inertial, and relaxed variants of Douglas-Rachford and ADMM algorithms for convex optimization, demonstrating improved computational performance on LASSO and logistic regression problems.

## Contribution

It develops novel inexact inertial-relaxed algorithms for Douglas-Rachford and ADMM, expanding their theoretical framework and practical efficiency.

## Key findings

- Improved computational performance on LASSO and logistic regression
- New inexact variants with inertial and overrelaxation features
- Theoretical analysis based on a new inexact proximal point framework

## Abstract

This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact version of the proximal point algorithm that includes both an inertial step and overrelaxation. We apply our new inexact ADMM method to LASSO and logistic regression problems and obtain somewhat better computational performance than earlier inexact ADMM methods.