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PENALTY METHODS WITH STOCHASTIC APPROXIMATION FOR STOCHASTIC NONLINEAR PROGRAMMING
Wang, Xiao1,2; Ma, Shiqian3; Yuan, Ya-Xiang4
2017-07-01
Source PublicationMATHEMATICS OF COMPUTATION
ISSN0025-5718
Volume86Issue:306Pages:1793-1820
AbstractIn this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via calls to a stochastic first-order or zeroth-order oracle. In each iteration of the proposed methods, we minimize an exact penalty function which is nonsmooth and nonconvex with only stochastic first-order or zeroth-order information available. Stochastic approximation algorithms are presented for solving this particular subproblem. The worst-case complexity of calls to the stochastic first-order (or zeroth-order) oracle for the proposed penalty methods for obtaining an epsilon-stochastic critical point is analyzed.
KeywordStochastic programming nonlinear programming stochastic approximation penalty method global complexity bound
DOI10.1090/mcom/3178
Language英语
Funding ProjectChinese University of Hong Kong[4055016] ; Hong Kong Research Grants Council General Research Fund Early Career Scheme[CUHK 439513] ; NSFC[11331012] ; NSFC[11321061] ; NSFC[11461161005] ; NSFC[11301505] ; UCAS President Grant[Y35101AY00] ; [119103S175]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000398823400011
PublisherAMER MATHEMATICAL SOC
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25271
Collection计算数学与科学工程计算研究所
Affiliation1.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
2.Chinese Acad Sci, Key Lab Big Data Min & Knowledge Management, Beijing, Peoples R China
3.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Wang, Xiao,Ma, Shiqian,Yuan, Ya-Xiang. PENALTY METHODS WITH STOCHASTIC APPROXIMATION FOR STOCHASTIC NONLINEAR PROGRAMMING[J]. MATHEMATICS OF COMPUTATION,2017,86(306):1793-1820.
APA Wang, Xiao,Ma, Shiqian,&Yuan, Ya-Xiang.(2017).PENALTY METHODS WITH STOCHASTIC APPROXIMATION FOR STOCHASTIC NONLINEAR PROGRAMMING.MATHEMATICS OF COMPUTATION,86(306),1793-1820.
MLA Wang, Xiao,et al."PENALTY METHODS WITH STOCHASTIC APPROXIMATION FOR STOCHASTIC NONLINEAR PROGRAMMING".MATHEMATICS OF COMPUTATION 86.306(2017):1793-1820.
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