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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（4）
• 页码范围: 795-808
• 页数: 14页
• 语种: 英文

摘要

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 the solution set,which is more reasonable than the previous bound.