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On The Linear Convergence Of The Alternating Direction Method Of Multipliers, Mingyi Hong, Zhi-Quan Luo Jul 2016

On The Linear Convergence Of The Alternating Direction Method Of Multipliers, Mingyi Hong, Zhi-Quan Luo

Industrial and Manufacturing Systems Engineering Publications

We analyze the convergence rate of the alternating direction method of multipliers (ADMM) for minimizing the sum of two or more nonsmooth convex separable functions subject to linear constraints. Previous analysis of the ADMM typically assumes that the objective function is the sum of only two convex functions defined on two separable blocks of variables even though the algorithm works well in numerical experiments for three or more blocks. Moreover, there has been no rate of convergence analysis for the ADMM without strong convexity in the objective function. In this paper we establish the global R-linear convergence of the ADMM ...