Sub-quadratic convergence of a smoothing Newton algorithm for the P(0) and monotone LCP

doi:10.1007/s10107-003-0457-8

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	Sub-quadratic convergence of a smoothing Newton algorithm for the P(0) and monotone LCP
	Huang, ZH ; Qi, LQ ; Sun, DF
	2004-04-01
发表期刊	MATHEMATICAL PROGRAMMING
ISSN	0025-5610
卷号	99 期号:3 页码:423-441
摘要	Given M is an element of R(nxn) and q is an element of R(n), the linear complementarity problem (LCP) is to find (x, s) is an element of R(n) x R(n) such that (x, s) greater than or equal to 0, s = M(x) + q, x(T)s = 0. By using the Chen-Harker-Kanzow-Sniale (CHKS) smoothing function, the LCP is reformulated as a system of parameterized smooth-nonsmooth equations. As a result, a smoothing Newton algorithm, which is a modified version of the Qi-Sun-Zhou algorithm [Matheniatical Programming, Vol. 87, 2000, pp. 1-35], is proposed to solve the LCP with M being assumed to be a P(0)-matrix (P(0)-LCP). The proposed algorithm needs only to solve one system of linear equations and to do one line search at each iteration. It is proved in this paper that the proposed algorithm has the following convergence properties: (i) it is well-defined and any accumulation point of the iteration sequence is a solution of the P(0)-LCP: (ii) it generates a bounded sequence if the P(0)-LCP has a nonempty and bounded solution set: (iii) if an accumulation point of the iteration sequence satisfies a nonsingularity condition, which implies the P(0)-LCP has a unique solution, then the whole iteration sequence converges to this accumulation point sub-quadratically with a Q-rate 2 - t, where t is an element of (0, 1) is a parameter; and (iv) if M is positive semidefinite and an accumulation point of the iteration sequence satisfies a strict complementarity condition, then the whole sequence converges to the accumulation point quadratically.
关键词	linear complementarity problem smoothing Newton method global convergence sub-quadratic convergence
DOI	10.1007/s10107-003-0457-8
语种	英语
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000220991700002
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/714
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, ZH
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China 2.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China 3.Natl Univ Singapore, Dept Math, Singapore 117543, Singapore
推荐引用方式 GB/T 7714	Huang, ZH,Qi, LQ,Sun, DF. Sub-quadratic convergence of a smoothing Newton algorithm for the P(0) and monotone LCP[J]. MATHEMATICAL PROGRAMMING,2004,99(3):423-441.
APA	Huang, ZH,Qi, LQ,&Sun, DF.(2004).Sub-quadratic convergence of a smoothing Newton algorithm for the P(0) and monotone LCP.MATHEMATICAL PROGRAMMING,99(3),423-441.
MLA	Huang, ZH,et al."Sub-quadratic convergence of a smoothing Newton algorithm for the P(0) and monotone LCP".MATHEMATICAL PROGRAMMING 99.3(2004):423-441.