This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter, and this primal illustration of ADMM is thus complemental to its dual illustration in the literature.Expand

This paper answers the question for the three-block case where there are three separable functions in the objective of the alternating direction method of multipliers, and shows that when one of them is strongly convex, the direct extension of ADMM is convergent.Expand

An augmented Lagrangian alternating direction method is employed to solve this convex and well-conditioned regularized subproblem, and two accelerating skills are also implemented.Expand

The convergence rate under a unified conceptual framework is proved, which includes the projection and contraction methods as special cases and thus perfects the theory of the existing projection and contracting methods.Expand

It is shown that when one function in the objective is strongly convex, the penalty parameter and the operators in the linear equality constraint are appropriately restricted, it is sufficient to guarantee the convergence of the direct extension of ADMM.Expand

This paper considers the generalized ADMM, which incorporates an acceleration factor and is more efficient, and proposes using the original ϵ-optimal solution measure, under which it is proved that the G-ADMM converges at a rate of O(1/t).Expand

The optimal lower bound of the proximal parameter is derived and result in the generalized ADMM with optimal indefinite proximal term is result and the global convergence and the iteration complexity of the proposed method are proved.Expand

It is proved that the sequence generated by the alternating direction method of multipliers converges locally to a critical point of the nonconvex optimization problem in alinear convergence rate, and the corresponding sequence of the augmented Lagrangian function value converges in a linear convergence rate.Expand