A regularized smoothing Newton method for box constrained variational inequality problems with P-0-functions

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	A regularized smoothing Newton method for box constrained variational inequality problems with P-0-functions
	Qi, HD
	2000-02-23
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	10 期号:2 页码:315-330
摘要	Based on Qi, Sun, and Zhou's smoothing Newton method, we propose a regularized smoothing Newton method for the box constrained variational inequality problem with P-0-function (P-0 BVI). The proposed algorithm generates an infinite sequence such that the value of the merit function converges to zero. If P-0 BVI has a nonempty bounded solution set, the iteration sequence must be bounded. This result implies that there exists at least one accumulation point. Under CD-regularity, we prove that the proposed algorithm has a superlinear (quadratic) convergence rate without requiring strict complementarity conditions. The main feature of our global convergence results is that we do not assume a priori the existence of an accumulation point. This assumption is used widely in the literature due to the possible unboundedness of level sets of various adopted merit functions. Preliminary numerical results are also reported.
关键词	smoothing Newton's method semismoothness global convergence superlinear convergence
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000085671900001
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/15545
专题	中国科学院数学与系统科学研究院
通讯作者	Qi, HD
作者单位	Chinese Acad Sci, Inst Computat Math & Sci Engn, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Qi, HD. A regularized smoothing Newton method for box constrained variational inequality problems with P-0-functions[J]. SIAM JOURNAL ON OPTIMIZATION,2000,10(2):315-330.
APA	Qi, HD.(2000).A regularized smoothing Newton method for box constrained variational inequality problems with P-0-functions.SIAM JOURNAL ON OPTIMIZATION,10(2),315-330.
MLA	Qi, HD."A regularized smoothing Newton method for box constrained variational inequality problems with P-0-functions".SIAM JOURNAL ON OPTIMIZATION 10.2(2000):315-330.