On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming

doi:10.1287/moor.2018.0939

	On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming
	Liu, Ya-Feng1 ; Liu, Xin2,3 ; Ma, Shiqian 4
	2019-05-01
发表期刊	MATHEMATICS OF OPERATIONS RESEARCH
ISSN	0364-765X
卷号	44 期号:2 页码:632-650
摘要	In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The stopping criterion used in solving the augmented Lagrangian subproblem in the proposed IAL framework is weaker and potentially much easier to check than the one used in most of the existing IAL frameworks/methods. We analyze the global convergence and the nonergodic convergence rate of the proposed IAL framework. Preliminary numerical results are presented to show the efficiency of the proposed IAL framework and the importance of the nonergodic convergence and convergence rate analysis.
关键词	inexact augmented Lagrangian framework nonergodic convergence rate composite convex programming
DOI	10.1287/moor.2018.0939
语种	英语
资助项目	National Natural Science Foundation of China (NSFC)[11631013] ; National Natural Science Foundation of China (NSFC)[11331012] ; National Natural Science Foundation of China (NSFC)[11671419] ; National Natural Science Foundation of China (NSFC)[11571221] ; Beijing Natural Science Foundation[L172020] ; NSFC[11622112] ; NSFC[11471325] ; NSFC[91530204] ; NSFC[11688101] ; National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences (CAS) ; Key Research Program of Frontier Sciences, CAS[QYZDJ-SSW-SYS010] ; Department of Mathematics at University of California, Davis
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000468403700011
出版者	INFORMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34719
专题	计算数学与科学工程计算研究所
通讯作者	Liu, Ya-Feng
作者单位	1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing, Peoples R China 2.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Acad Math & Syst Sci, Beijing, Peoples R China 3.Univ Chinese Acad Sci, Beijing, Peoples R China 4.Univ Calif Davis, Dept Math, Davis, CA 95616 USA
推荐引用方式 GB/T 7714	Liu, Ya-Feng,Liu, Xin,Ma, Shiqian. On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming[J]. MATHEMATICS OF OPERATIONS RESEARCH,2019,44(2):632-650.
APA	Liu, Ya-Feng,Liu, Xin,&Ma, Shiqian.(2019).On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming.MATHEMATICS OF OPERATIONS RESEARCH,44(2),632-650.
MLA	Liu, Ya-Feng,et al."On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming".MATHEMATICS OF OPERATIONS RESEARCH 44.2(2019):632-650.