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The alternating direction method of multipliers (ADMM) is a widely usedmethod for solving many convex minimization models arising in signal and imageprocessing. In this paper, we propose an inertial ADMM for solving a two-blockseparable convex minimization problem with linear equality constraints. Thisalgorithm is obtained by making use of the inertial Douglas-Rachford splittingalgorithm to the corresponding dual of the primal problem. We study theconvergence analysis of the proposed algorithm in infinite-dimensional Hilbertspaces. Furthermore, we apply the proposed algorithm on the robust principalcomponent pursuit problem and also compare it with other state-of-the-artalgorithms. Numerical results demonstrate the advantage of the proposedalgorithm.

An inertial alternating direction method of multipliers for solving a two-block separable convex minimization problem