On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming | |
Liu, Ya-Feng2; Liu, Xin1,3; Ma, Shiqian4 | |
刊名 | MATHEMATICS OF OPERATIONS RESEARCH |
2019-05-01 | |
卷号 | 44期号:2页码:632-650 |
关键词 | inexact augmented Lagrangian framework nonergodic convergence rate composite convex programming |
ISSN号 | 0364-765X |
DOI | 10.1287/moor.2018.0939 |
英文摘要 | 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. |
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 |
语种 | 英语 |
出版者 | INFORMS |
WOS记录号 | WOS:000468403700011 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/34718] |
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.Univ Chinese Acad Sci, Beijing, Peoples R China 2.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing, Peoples R China 3.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Acad Math & Syst 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. |
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