  We study the convergence of the Augmented Decomposition Algorithm (ADA)
proposed in [32] for solving multi-block separable convex minimization problems
subject to linear constraints. We show that the global convergence rate of the
exact ADA is o(1/k) under the assumption that there exists a saddle point. We
consider the inexact Augmented Decomposition Algorithm (iADA) and establish
global and local convergence results under some mild assumptions, by providing
a stability result for the maximal monotone operator T associated with the
perturbation from both primal and dual perspectives. This result implies the
local linear convergence of the inexact ADA for many applications such as the
lasso, total variation reconstruction, exchange problem and many other problems
from statistics, machine learning and engineering with l1 regularization.

Optimization and Control