TY - JOUR
T1 - A Fast Symmetric Alternating Direction Method of Multipliers
AU - Luo , Gang
AU - Yang , Qingzhi
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 200
EP - 219
PY - 2019
DA - 2019/12
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2018-0108
UR - https://global-sci.org/intro/article_detail/nmtma/13437.html
KW - Nesterov's accelerating strategy, alternating direction method of multipliers, symmetric ADMM,  separable linear constrained optimization.
AB - <p style="text-align: justify;">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&#39;s accelerating strategy, an accelerated symmetric ADMM is proposed. We prove its $\mathcal{O}(\frac{1}{k^2})$ convergence rate under strongly convex condition. For the general situation, an accelerated method with a restart rule is proposed. Some preliminary numerical experiments show the efficiency of our algorithms.</p>