The alternating direction method of multipliers (ADMM) has been widely used for solving structured convex optimization problems.In particular,the ADMM can solve convex programs that minimize the sum of N convex functions with N-block variables linked by some linear constraints.While the convergence of the ADMM for N=2 was well established in the literature,it remained an open problem for a long time whether or not the ADMM for N ≥ 3 is still convergent until very recently.