O(1/t) complexity analysis of the generalized alternating direction method of multipliers

Owing to its efficiency in solving some types of large-scale separable optimization problems with linear constraints, the convergence rate of the alternating direction method of multipliers (ADMM for short) has recently attracted significant attention. In this paper, we consider the generalized ADMM (G-ADMM), which incorporates an acceleration factor and is more efficient. Instead of using a solution measure that depends on a bounded set and cannot be easily estimated, we propose using the original E-optimal solution measure, under which we prove that the G-ADMM converges at a rate of O(1/t). The new bound depends on the penalty parameter and the distance between the initial point and solution set, which is more reasonable than the previous bound.