KMS Of Academy of mathematics and systems sciences, CAS
| PENALTY METHODS WITH STOCHASTIC APPROXIMATION FOR STOCHASTIC NONLINEAR PROGRAMMING | |
Wang, Xiao1,2; Ma, Shiqian3; Yuan, Ya-Xiang4
| |
| 2017-07-01 | |
| Source Publication | MATHEMATICS OF COMPUTATION
 |
| ISSN | 0025-5718 |
| Volume | 86Issue:306Pages:1793-1820 |
| Abstract | 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. |
| Keyword | Stochastic programming nonlinear programming stochastic approximation penalty method global complexity bound |
| DOI | 10.1090/mcom/3178 |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000398823400011 |
| Publisher | AMER MATHEMATICAL SOC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/25271 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Wang, Xiao |
| Affiliation | 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 |
| 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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