  We present a novel framework, namely AADMM, for acceleration of linearized
alternating direction method of multipliers (ADMM). The basic idea of AADMM is
to incorporate a multi-step acceleration scheme into linearized ADMM. We
demonstrate that for solving a class of convex composite optimization with
linear constraints, the rate of convergence of AADMM is better than that of
linearized ADMM, in terms of their dependence on the Lipschitz constant of the
smooth component. Moreover, AADMM is capable to deal with the situation when
the feasible region is unbounded, as long as the corresponding saddle point
problem has a solution. A backtracking algorithm is also proposed for practical
performance.
