南方科技大学知识苑(SUSTech KC): A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING

题名	A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING
作者	He, Bingsheng 1; Ma, Feng 2; Xu, Shengjie3,4 ; Yuan, Xiaoming 5
通讯作者	He, Bingsheng
发表日期	2023-02-01
DOI	10.1090/mcom/3822
发表期刊	MATHEMATICS OF COMPUTATION 影响因子和分区
ISSN	0025-5718
EISSN	1088-6842
卷号	92 期号:342页码:1633-1663
摘要	The augmented Lagrangian method (ALM) is classic for canoni-cal convex programming problems with linear constraints, and it finds many applications in various scientific computing areas. A major advantage of the ALM is that the step for updating the dual variable can be further relaxed with a step size in (0, 2), and this advantage can easily lead to numerical ac-celeration for the ALM. When a separable convex programming problem is discussed and a corresponding splitting version of the classic ALM is consid-ered, convergence may not be guaranteed and thus it is seemingly impossible that a step size in (0,2) can be carried on to the relaxation step for updating the dual variable. We show that for a parallel splitting version of the ALM, a step size in (0,2) can be maintained for further relaxing both the primal and dual variables if the relaxation step is simply corrected by a rank-two matrix. Hence, a rank-two relaxed parallel splitting version of the ALM with a step size in (0,2) is proposed for separable convex programming problems. We validate that the new algorithm can numerically outperform existing algorithms of the same kind significantly by testing some applications.
关键词	Convex programming scientific computing augmented Lagrangian method parallel splitting step size
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	其他
资助项目	NSFC["11871029","12171481","11871264"]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000941193400001
出版者	AMER MATHEMATICAL SOC
ESI学科分类	MATHEMATICS
Scopus记录号	2-s2.0-85152642562
来源库	Web of Science
引用统计	被引频次[WOS]：0
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/502118
专题	理学院_数学系
作者单位	1.Nanjing Univ, Dept Math, Nanjing, Peoples R China 2.High Tech Inst Xian, Xian 710025, Shaanxi, Peoples R China 3.Harbin Inst Technol, Dept Math, Harbin, Peoples R China 4.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China 5.Univ Hong Kong, Dept Math, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	He, Bingsheng,Ma, Feng,Xu, Shengjie,et al. A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING[J]. MATHEMATICS OF COMPUTATION,2023,92(342):1633-1663.
APA	He, Bingsheng,Ma, Feng,Xu, Shengjie,&Yuan, Xiaoming.(2023).A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING.MATHEMATICS OF COMPUTATION,92(342),1633-1663.
MLA	He, Bingsheng,et al."A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING".MATHEMATICS OF COMPUTATION 92.342(2023):1633-1663.