A Fast Symmetric Alternating Direction Method of Multipliers

global sci
2020 Numerical Mathematics: Theory, Methods and Applications  
In recent years, alternating direction method of multipliers (ADMM) and its variants are popular for the extensive use in image processing and statistical learning. A variant of ADMM: symmetric ADMM, which updates the Lagrange multiplier twice in one iteration, is always faster whenever it converges. In this paper, combined with Nesterov's accelerating strategy, an accelerated symmetric ADMM is proposed. We prove its O( 1 k 2 ) convergence rate under strongly convex condition. For the general
more » ... . For the general situation, an accelerated method with a restart rule is proposed. Some preliminary numerical experiments show the efficiency of our algorithms. AMS subject classifications: 90C25, 90C30, 49M29, 65B99
doi:10.4208/nmtma.oa-2018-0108 fatcat:3kuezhps4zf3lnecsxwihk7aaa