A smoothing Newton method for extended vertical linear complementarity problems

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	A smoothing Newton method for extended vertical linear complementarity problems
	Qi, HD ; Liao, LZ
	1999-10-27
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	21 期号:1 页码:45-66
摘要	In this paper, we reformulate the extended vertical linear complementarity problem (EVLCP(m, q)) as a nonsmooth equation H(t, x) = 0, where H : Rn+1 --> Rn+1, t is an element of R is a parameter variable, and x is an element of R is the original variable. H is continuously differentiable except at such points (t, x) with t = 0. Furthermore H is strongly semismooth. The reformulation of EVLCP(m; q) as a nonsmooth equation is based on the so-called aggregation (smoothing) function. As a result, a Newton-type method is proposed which generates a sequence {w(k) = (t(k), x(k))} with all t(k) > 0. We prove that every accumulation point of this sequence is a solution of EVLCP(M,q) under the assumption of row W-0-property. If row W-property holds at the solution point, then the convergence rate is quadratic. Promising numerical results are also presented.
关键词	aggregation function smoothing Newton method semismoothness global convergence
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000083320600003
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/14127
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	1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong
推荐引用方式 GB/T 7714	Qi, HD,Liao, LZ. A smoothing Newton method for extended vertical linear complementarity problems[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,1999,21(1):45-66.
APA	Qi, HD,&Liao, LZ.(1999).A smoothing Newton method for extended vertical linear complementarity problems.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,21(1),45-66.
MLA	Qi, HD,et al."A smoothing Newton method for extended vertical linear complementarity problems".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 21.1(1999):45-66.