Convergence Study on the Proximal Alternating Direction Method with Larger Step Size
نویسندگان
چکیده
The alternating direction method of multipliers (ADMM) is a popular method for the separable convex programming with linear constraints, and the proximal ADMM is its important variant. Previous studies show that the relaxation factor γ ∈ (0, 1+ √ 5 2 ) by Fortin and Glowinski for the ADMM is also valid for the proximal ADMM. In this paper, we further demonstrate that the feasible region of γ depends on the proximal term added on the second subproblem, and can be enlarged when the proximal factor is positive. We derive the exact relationship between the relaxation factor γ and the proximal factor. Finally, we prove the global convergence and derive a worst-case O(1/t) convergence rate in the ergodic sense for this generalized scheme.
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تاریخ انتشار 2017