Bounded perturbation resilience of extragradient-type methods and their applications

doi:10.1186/s13660-017-1555-0

	Bounded perturbation resilience of extragradient-type methods and their applications
	Dong,Q-L 1; Gibali,A 2; Jiang,D 1; Tang,Y 3
刊名	Journal of Inequalities and Applications
	2017-11-10
卷号	2017 期号:1
关键词	inertial-type method bounded perturbation resilience extragradient method subgradient extragradient method variational inequality 49J35 58E35 65K15 90C47
ISSN号	1029-242X
DOI	10.1186/s13660-017-1555-0
英文摘要	AbstractIn this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving a variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning that an inexact version of the methods can also be considered. Moreover, once an algorithm is proved to be bounded perturbation resilience, superiorization can be used, and this allows flexibility in choosing the bounded perturbations in order to obtain a superior solution, as well explained in the paper. We also discuss some inertial extragradient methods. Under mild and standard assumptions of monotonicity and Lipschitz continuity of the VI’s associated mapping, convergence of the perturbed extragradient and subgradient extragradient methods is proved. In addition we show that the perturbed algorithms converge at the rate of O(1/t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(1/t)$\end{document}. Numerical illustrations are given to demonstrate the performances of the algorithms.
语种	英语
出版者	Springer International Publishing
WOS记录号	BMC:10.1186/S13660-017-1555-0
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/395]
专题	中国科学院数学与系统科学研究院
通讯作者	Gibali,A
作者单位	1. 2. 3.
推荐引用方式 GB/T 7714	Dong,Q-L,Gibali,A,Jiang,D,et al. Bounded perturbation resilience of extragradient-type methods and their applications[J]. Journal of Inequalities and Applications,2017,2017(1).
APA	Dong,Q-L,Gibali,A,Jiang,D,&Tang,Y.(2017).Bounded perturbation resilience of extragradient-type methods and their applications.Journal of Inequalities and Applications,2017(1).
MLA	Dong,Q-L,et al."Bounded perturbation resilience of extragradient-type methods and their applications".Journal of Inequalities and Applications 2017.1(2017).