  In this paper, we establish the convergence properties for a majorized
alternating direction method of multipliers (ADMM) for linearly constrained
convex optimization problems whose objectives contain coupled functions. Our
convergence analysis relies on the generalized Mean-Value Theorem which plays
an important role to properly control the cross terms due to the presence of
coupled objective functions. Our results in particular show that directly
applying 2-block ADMM with a large step length to the linearly constrained
convex optimization problem with a quadratically coupled objective function is
convergent under mild conditions. We also provide several iteration complexity
results for the algorithm.
