A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming

doi:10.1016/j.cam.2019.02.028

CORC > 兰州理工大学 > 兰州理工大学 > 理学院

	A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming
	Chang, Xiaokai 1,2; Liu, Sanyang 1; Zhao, Pengjun 3; Song, Dunjiang 4,5
刊名	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
	2019-09
卷号	357 页码:251-272
关键词	Alternating direction method of multipliers Proximal point algorithm Separable convex programming Linearization Indefinite proximal regularization LASSO
ISSN号	0377-0427
DOI	10.1016/j.cam.2019.02.028
英文摘要	The linearized alternating direction method of multipliers (ADMM), with indefinite proximal regularization, has been proved to be efficient for solving separable convex optimization subject to linear constraints. In this paper, we present a generalization of linearized ADMM (G-LADMM) to solve two-block separable convex minimization model, which linearizes all the subproblems by choosing a proper positive-definite or indefinite proximal term and updates the Lagrangian multiplier twice in different ways. Furthermore, the proposed G-LADMM can be expressed as a proximal point algorithm (PPA), and all the subproblems are just to estimate the proximity operator of the function in the objective. We specify the domain of the proximal parameter and stepsizes to guarantee that G-LADMM is globally convergent. It turns out that our convergence domain of the proximal parameter and stepsizes is significantly larger than other convergence domains in the literature. The numerical experiments illustrate the improvements of the proposed G-LADMM to solve LASSO and image decomposition problems. (C) 2019 Elsevier B.V. All rights reserved.
资助项目	National Natural Science Foundation of China[61877046] ; National Natural Science Foundation of China[41471338]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000465168400016
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/31624]
专题	理学院
通讯作者	Chang, Xiaokai
作者单位	1.Xidian Univ, Sch Math & Stat, Xian 710071, Peoples R China 2.Lanzhou Univ Technol, Coll Sci, Lanzhou 730050, Gansu, Peoples R China 3.Shangluo Univ, Sch Math & Comp Applicat, Shangluo 726000, Peoples R China 4.Chinese Acad Sci, Inst Sci, Beijing 100190, Peoples R China 5.Chinese Acad Sci, Inst Dev, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Chang, Xiaokai,Liu, Sanyang,Zhao, Pengjun,et al. A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2019,357:251-272.
APA	Chang, Xiaokai,Liu, Sanyang,Zhao, Pengjun,&Song, Dunjiang.(2019).A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,357,251-272.
MLA	Chang, Xiaokai,et al."A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 357(2019):251-272.