  In this paper, we consider the linearly constrained composite convex
optimization problem, whose objective is a sum of a smooth function and a
possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL)
framework for solving the problem. The stopping criterion used in solving the
augmented Lagrangian (AL) subproblem in the proposed IAL framework is weaker
and potentially much easier to check than the one used in most of the existing
IAL frameworks/methods. We analyze the global convergence and the non-ergodic
convergence rate of the proposed IAL framework.
