A note on the convergence of alternating proximal gradient method

We consider a class of linearly constrained separable convex programming problems whose objective functions are the sum of m   convex functions without coupled variables. The alternating proximal gradient method is an effective method for the case m=2m=2, but it is unknown whether its convergence can be extended to the general case m⩾3m⩾3. This note shows the global convergence of this extension when the involved functions are strongly convex.