  In the present paper we propose a novel convergence analysis of the
Alternating Direction Methods of Multipliers (ADMM), based on its equivalence
with the overrelaxed Primal-Dual Hybrid Gradient (oPDHG) algorithm. We consider
the smooth case, which correspond to the cas where the objective function can
be decomposed into one differentiable with Lipschitz continuous gradient part
and one strongly convex part. An accelerated variant of the ADMM is also
proposed, which is shown to converge linearly with same rate as the oPDHG.
