  The alternating direction method of multipliers (ADMM) is a widely used
method for solving many convex minimization models arising in signal and image
processing. In this paper, we propose an inertial ADMM for solving a two-block
separable convex minimization problem with linear equality constraints. This
algorithm is obtained by making use of the inertial Douglas-Rachford splitting
algorithm to the corresponding dual of the primal problem. We study the
convergence analysis of the proposed algorithm in infinite-dimensional Hilbert
spaces. Furthermore, we apply the proposed algorithm on the robust principal
component pursuit problem and also compare it with other state-of-the-art
algorithms. Numerical results demonstrate the advantage of the proposed
algorithm.
