The alternating direction method of multipliers (ADMM) is a benchmark for solving two-block separable convex programs, and it finds more and more applications in many areas. However, as other first-order methods, ADMM also suffers from low convergence. In this paper, to accelerate the convergence of ADMM, we relax the restriction region of the Fortin and Glowinski’s constant γ in ADMM from (0, 1+ √ 5 2 ) to (0,+∞), and thus get a proximal ADMM with larger step size. Then, to further accelerate its efficiency, we use the convex combination of its output with the current iterate to generate the new iterate. Under mild conditions, we prove the global convergence of the new method. Some numerical experiments are given to demonstrate the advantage of large step size.
View Proximal ADMM with larger step size for two-block separable convex programs