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

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.