A Note on the Alternating Direction Method of Multipliers

We consider the linearly constrained separable convex programming, whose objective function is separable into m individual convex functions without coupled variables. The alternating direction method of multipliers has been well studied in the literature for the special case m=2, while it remains open whether its convergence can be extended to the general case ma parts per thousand yen3. This note shows the global convergence of this extension when the involved functions are further assumed to be strongly convex.