On the linear convergence of the alternating direction method of multipliers

• Published in: Mathematical programming Vol. 162; no. 1-2; pp. 165 - 199
• Main Authors: Hong, Mingyi, Luo, Zhi-Quan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017; Springer Nature B.V
• Subjects: Algorithms; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Convergence; Convex analysis; Convexity; Decomposition; Errors; Feasibility; Full Length Paper; Inequality; Lagrange multiplier; Linear programming; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical models; Mathematics; Mathematics and Statistics; Mathematics of Computing; Methods; Multipliers; Numerical Analysis; Optimization; Studies; Texts; Theoretical; Error bound; Linear convergence; Dual ascent; 49; Alternating directions of multipliers; 90

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 conve...