| 求解两块可分离凸极小化问题的惯性交替方向乘子法 |
| |
| 引用本文： | 杨洋,唐玉超.求解两块可分离凸极小化问题的惯性交替方向乘子法[J].数学研究及应用,2021,41(2):204-220. |
| |
| 作者姓名： | 杨洋 唐玉超 |
| |
| 作者单位： | 南昌大学数学系, 江西 南昌 330031 |
| |
| 基金项目： | 国家自然科学基金(Grant Nos.12061045; 12061046; 11661056; 11771198; 11771347; 91730306; 41390454; 11401293), 中国博士后科学基金(Grant No.2015M571989), 江西省博士后科学基金(Grant No.2015KY51). |
| |
| 摘 要： | The alternating direction method of multipliers(ADMM)is a widely used method for solving many convex minimization models arising in signal and image processing.In this paper,we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints.This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem.We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces.Furthermore,we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms.Numerical results demonstrate the advantage of the proposed algorithm.
|
| 关 键 词： | alternating direction method of multipliers inertial method Douglas-Rachford splitting algorithm |
| 收稿时间： | 2020/3/12 0:00:00 |
| 修稿时间： | 2020/9/27 0:00:00 |
An Inertial Alternating Direction Method of Multipliers for Solving a Two-Block Separable Convex Minimization Problem |
| |
| Yang YANG,Yuchao TANG.An Inertial Alternating Direction Method of Multipliers for Solving a Two-Block Separable Convex Minimization Problem[J].Journal of Mathematical Research with Applications,2021,41(2):204-220. |
| |
| Authors: | Yang YANG Yuchao TANG |
| |
| Institution: | Department of Mathematics, Nanchang University, Jiangxi 330031, P. R. China |
| |
| Abstract: | The alternating direction method of multipliers (ADMM) is a widely used method for solving many convex minimization models arising in signal and image processing. In this paper, we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints. This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem. We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces. Furthermore, we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms. Numerical results demonstrate the advantage of the proposed algorithm. |
| |
| Keywords: | alternating direction method of multipliers inertial method Douglas-Rachford splitting algorithm |
| 本文献已被 维普 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |
