Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Penalty methods with stochastic approximation for stochastic nonlinear programming
HTML articles powered by AMS MathViewer

by Xiao Wang, Shiqian Ma and Ya-xiang Yuan PDF
Math. Comp. 86 (2017), 1793-1820 Request permission

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.
References
Similar Articles
Additional Information
  • Xiao Wang
  • Affiliation: School of Mathematical Sciences, University of Chinese Academy of Sciences; Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, People’s Republic of China
  • Email: wangxiao@ucas.ac.cn
  • Shiqian Ma
  • Affiliation: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong
  • MR Author ID: 826033
  • Email: sqma@se.cuhk.edu.hk
  • Ya-xiang Yuan
  • Affiliation: State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, People’s Republic of China
  • Email: yyx@lsec.cc.ac.cn
  • Received by editor(s): April 8, 2015
  • Received by editor(s) in revised form: December 1, 2015
  • Published electronically: October 12, 2016
  • Additional Notes: The research of the first author was supported in part by Postdoc Grant 119103S175, UCAS President Grant Y35101AY00 and NSFC Grant 11301505.
    The research of the second author was supported in part by a Direct Grant of the Chinese University of Hong Kong (Project ID: 4055016) and the Hong Kong Research Grants Council General Research Fund Early Career Scheme (Project ID: CUHK 439513)
    The research of the third author was supported in part by NSFC Grants 11331012, 11321061 and 11461161005
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1793-1820
  • MSC (2010): Primary 90C15, 90C30, 62L20, 90C60
  • DOI: https://doi.org/10.1090/mcom/3178
  • MathSciNet review: 3626537