Existence and limiting behavior of a non-interior-point trajectory for nonlinear complementarity problems without strict feasibility condition

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	Existence and limiting behavior of a non-interior-point trajectory for nonlinear complementarity problems without strict feasibility condition
	Zhao, YB; Li, D
	2001-11-19
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	40 期号:3 页码:898-924
摘要	For P-0-complementarity problems, most existing non-interior-point path-following methods require the existence of a strictly feasible point. (For a P--complementarity problem, the existence of a strictly feasible point is equivalent to the nonemptyness and the boundedness of the solution set.) In this paper, we propose a new homotopy formulation for complementarity problems by which a new non interior-point continuation trajectory is generated. The existence and the boundedness of this non interior-point trajectory for P-0-complementarity problems are proved under a very mild condition that is weaker than most conditions used in the literature. One prominent feature of this condition is that it may hold even when the often-assumed strict feasibility condition fails to hold. In particular, for a P--problem it turns out that the new non interior-point trajectory exists and is bounded if and only if the problem has a solution. We also study the convergence of this trajectory and characterize its limiting point as the parameter approaches zero.
关键词	complementarity problems non-interior-point methods homotopy continuation trajectories P-0-functions P-*-functions
语种	英语
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000172406300011
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/16852
专题	中国科学院数学与系统科学研究院
通讯作者	Zhao, YB
作者单位	Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhao, YB,Li, D. Existence and limiting behavior of a non-interior-point trajectory for nonlinear complementarity problems without strict feasibility condition[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2001,40(3):898-924.
APA	Zhao, YB,&Li, D.(2001).Existence and limiting behavior of a non-interior-point trajectory for nonlinear complementarity problems without strict feasibility condition.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,40(3),898-924.
MLA	Zhao, YB,et al."Existence and limiting behavior of a non-interior-point trajectory for nonlinear complementarity problems without strict feasibility condition".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 40.3(2001):898-924.