  Inexact alternating direction multiplier methods (ADMMs) are developed for
solving general separable convex optimization problems with a linear constraint
and with an objective that is the sum of smooth and nonsmooth terms. The
approach involves linearized subproblems, a back substitution step, and either
gradient or accelerated gradient techniques. Global convergence is established.
The methods are particularly useful when the ADMM subproblems do not have
closed form solution or when the solution of the subproblems is expensive.
Numerical experiments based on image reconstruction problems show the
effectiveness of the proposed methods.
