2017/05/17 by Adona, V. A., Goncalves, M. L. N., Melo, J. G.
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1705.06191
This paper analyzes the iteration-complexity of a generalized alternating direction method of multipliers (G-ADMM) for solving linearly constrained convex problems. This ADMM variant, which was first proposed by Bertsekas and Eckstein, introduces a relaxation parameter α∈ (0,2) into the second ADMM subproblem. Our approach is to show that the G-ADMM is an instance of a hybrid proximal extragradient framework with some special properties, and, as a by product, we obtain ergodic iteration-complexity for the G-ADMM with α∈ (0,2], improving and complementing related results in the literature. Additionally, we also present pointwise iteration-complexity for the G-ADMM.