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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.
Author Details
-
A Low-Rank and Sparse Decomposition-Based Method of Improving the Accuracy of Sub-Pixel Grayscale Centroid Extraction for Spot Images
Dong, Zhixu | Sun, Xingwei | Xu, Fangsu | Liu, WeijunIEEE Sensors Journal, Vol. 20 (2020), Iss. 11 P.5845
https://doi.org/10.1109/JSEN.2020.2974725 [Citations: 18] -
An Improvement of the Alternating Direction Method of Multipliers to Solve the Convex Optimization Problem
Peng, Jingjing | Wang, Zhijie | Yu, Siting | Tang, ZengaoMathematics, Vol. 13 (2025), Iss. 5 P.811
https://doi.org/10.3390/math13050811 [Citations: 0] -
An iterative reconstruction algorithm for unsupervised PET image
Wang, Siqi | Liu, Bing | Xie, Furan | Chai, LiPhysics in Medicine & Biology, Vol. 69 (2024), Iss. 5 P.055025
https://doi.org/10.1088/1361-6560/ad2882 [Citations: 0]