A relative-error inexact ADMM splitting algorithm for convex optimization with inertial effects

TL;DR

This paper introduces a novel inexact ADMM algorithm with relative error tolerance for convex optimization, proving its convergence and complexity, and demonstrating its effectiveness through preliminary regression experiments.

Contribution

It presents a new inexact ADMM variant with inertial effects, providing convergence proofs and complexity analysis, along with initial numerical validation.

Findings

Proven asymptotic convergence of the algorithm.

Established pointwise and ergodic iteration complexities.

Numerical experiments show effectiveness on regression problems.

Abstract

We propose a new relative-error inexact version of the alternating direction method of multipliers (ADMM) for convex optimization. We prove the asymptotic convergence of our main algorithm as well as pointwise and ergodic iteration-complexities for residuals. We also justify the effectiveness of the proposed algorithm through some preliminary numerical experiments on regression problems.