Year: 2020
Author: Qingzhi Yang, Gang Luo, Qingzhi Yang
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 1 : pp. 200–219
Abstract
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 $\mathcal{O}(\frac{1}{k^2})$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2018-0108
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 1 : pp. 200–219
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Nesterov's accelerating strategy alternating direction method of multipliers symmetric ADMM separable linear constrained optimization.
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