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DOI: 10.23952/cot.2025.45
Received June 21, 2024; Accepted September 17, 2024; Published online October 8, 2025
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.
How to Cite this Article:
M. Marques Alves, M. Geremia, A relative-error inexact ADMM splitting algorithm for convex optimization with inertial effects, Commun. Optim. Theory 2025 (2025) 45.