A GAUSS-SEIDEL TYPE METHOD FOR DYNAMIC NONLINEAR COMPLEMENTARITY PROBLEMS

doi:10.1137/19M1268884

CSpace

	A GAUSS-SEIDEL TYPE METHOD FOR DYNAMIC NONLINEAR COMPLEMENTARITY PROBLEMS
	Wu, Shu-Lin 1; Zhou, Tao 2; Chen, Xiaojun 3
	2020
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	58 期号:6 页码:3389-3412
摘要	The dynamic nonlinear complementarity problem (DNCP) consisting of a nonlinear differential system and a complementarity system has been used to formulate and study many dynamic problems. In a Gauss-Seidel type method for DNCPs, by first guessing a solution of the differential system, we can solve the complementarity system and then with the computed solution we can solve the differential system to update the guess. Upon convergence at the current time point we can move to the next one. The idea can be easily generalized to a multipoint version: instead of doing iterations at each single time point, we can do iterations for a number of time points, say J time points, all at once. Despite its simplicity and easy implementation, convergence of this method is not justified so far. In this paper, we present interesting convergence theorems for this method. We show that the method with a fixed length of time interval converges superlinearly and the convergence rate is robust with respect to the step-size h. Moreover, we show that the method with a fixed number of time points converges with a rate O(h). Since at each iteration the differential system and the complementarity system are solved separately, many existing solvers are directly applicable for each of these two systems. It is notable that we can solve the complementarity system at all the J time points in parallel. Numerical results of the method to solve the 4-diode bridge wave rectifier with random circuit parameters and the projected dynamic systems are given to support our findings.
关键词	dynamic nonlinear complementarity problems iterative methods convergence analysis nonsmooth circuit systems projected dynamic systems
DOI	10.1137/19M1268884
收录类别	SCI
语种	英语
资助项目	NSF of China[11771313] ; NSF of China[11822111] ; NSF of China[11688101] ; NSF of Sichuan Province[2018JY0469] ; Science Challenge Project[TZ2018001] ; Youth Innovation Promotion Association (CAS) ; Hong Kong Research Grant Council[PolyU153001/18P]
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000600685600015
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57871
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, Shu-Lin
作者单位	1.Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China 2.Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 3.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Wu, Shu-Lin,Zhou, Tao,Chen, Xiaojun. A GAUSS-SEIDEL TYPE METHOD FOR DYNAMIC NONLINEAR COMPLEMENTARITY PROBLEMS[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2020,58(6):3389-3412.
APA	Wu, Shu-Lin,Zhou, Tao,&Chen, Xiaojun.(2020).A GAUSS-SEIDEL TYPE METHOD FOR DYNAMIC NONLINEAR COMPLEMENTARITY PROBLEMS.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,58(6),3389-3412.
MLA	Wu, Shu-Lin,et al."A GAUSS-SEIDEL TYPE METHOD FOR DYNAMIC NONLINEAR COMPLEMENTARITY PROBLEMS".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 58.6(2020):3389-3412.