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A proximal point algorithm revisit on the alternating direction method of multipliers
TLDR
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.
The direct extension of ADMM for three-block separable convex minimization models is convergent when one function is strongly convex
TLDR
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.
Nonnegative tensor factorizations using an alternating direction method
TLDR
An augmented Lagrangian alternating direction method is employed to solve this convex and well-conditioned regularized subproblem, and two accelerating skills are also implemented.
On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators
TLDR
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.
On the convergence of the direct extension of ADMM for three-block separable convex minimization models with one strongly convex function
TLDR
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.
O(1/t) complexity analysis of the generalized alternating direction method of multipliers
TLDR
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).
Generalized ADMM with optimal indefinite proximal term for linearly constrained convex optimization
TLDR
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.
Local Linear Convergence of the Alternating Direction Method of Multipliers for Nonconvex Separable Optimization Problems
TLDR
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.
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