PENALTY METHODS WITH STOCHASTIC APPROXIMATION FOR STOCHASTIC NONLINEAR PROGRAMMING

doi:10.1090/mcom/3178

	PENALTY METHODS WITH STOCHASTIC APPROXIMATION FOR STOCHASTIC NONLINEAR PROGRAMMING
	Wang, Xiao 1,2; Ma, Shiqian 3; Yuan, Ya-Xiang4
	2017-07-01
发表期刊	MATHEMATICS OF COMPUTATION
ISSN	0025-5718
卷号	86 期号:306 页码:1793-1820
摘要	In 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.
关键词	Stochastic programming nonlinear programming stochastic approximation penalty method global complexity bound
DOI	10.1090/mcom/3178
语种	英语
资助项目	Chinese 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000398823400011
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25271
专题	计算数学与科学工程计算研究所
通讯作者	Wang, Xiao
作者单位	1.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
推荐引用方式 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.