A Projected Extrapolated Gradient Method with Larger Step Size for Monotone Variational Inequalities

doi:10.1007/s10957-021-01902-2

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	A Projected Extrapolated Gradient Method with Larger Step Size for Monotone Variational Inequalities
	Chang, Xiaokai 2; Bai, Jianchao 1
刊名	JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
	2021-08
卷号	190 期号:2 页码:602-627
关键词	Variational inequality Projected gradient method Convex optimization Predict-correct step size
ISSN号	0022-3239
DOI	10.1007/s10957-021-01902-2
英文摘要	A projected extrapolated gradient method is designed for solving monotone variational inequality in Hilbert space. Requiring local Lipschitz continuity of the operator, our proposed method improves the value of the extrapolated parameter and admits larger step sizes, which are predicted based a local information of the involved operator and corrected by bounding the distance between each pair of successive iterates. The correction will be implemented when the distance is larger than a given constant and its main cost is to compute a projection onto the feasible set. In particular, when the operator is the gradient of a convex function, the correction step is not necessary. We establish the convergence and ergodic convergence rate in theory under the larger range of parameters. Related numerical experiments illustrate the improvements in efficiency from the larger step sizes.
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER/PLENUM PUBLISHERS
WOS记录号	WOS:000674217900003
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/148889]
专题	理学院
作者单位	1.Northwestern Polytech Univ, Sch Math & Stat, Xian, Peoples R China 2.Lanzhou Univ Technol, Sch Sci, Lanzhou, Peoples R China;
推荐引用方式 GB/T 7714	Chang, Xiaokai,Bai, Jianchao. A Projected Extrapolated Gradient Method with Larger Step Size for Monotone Variational Inequalities[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,2021,190(2):602-627.
APA	Chang, Xiaokai,&Bai, Jianchao.(2021).A Projected Extrapolated Gradient Method with Larger Step Size for Monotone Variational Inequalities.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,190(2),602-627.
MLA	Chang, Xiaokai,et al."A Projected Extrapolated Gradient Method with Larger Step Size for Monotone Variational Inequalities".JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 190.2(2021):602-627.