On a new homotopy continuation trajectory for nonlinear complementarity problems

CSpace

	On a new homotopy continuation trajectory for nonlinear complementarity problems
	Zhao, YB ; Li, D
	2001-02-01
发表期刊	MATHEMATICS OF OPERATIONS RESEARCH
ISSN	0364-765X
卷号	26 期号:1 页码:119-146
摘要	Most known continuation methods for P-0 complementarity problems require some restrictive assumptions, such as the strictly feasible condition and the properness condition, to guarantee the existence and the boundedness of certain homotopy continuation trajectory. To relax such restrictions, we propose a new homotopy formulation for the complementarity problem based on which a new homotopy continuation trajectory is generated. For P-0 complementarity problems, the most promising feature of this trajectory is the assurance of the existence and the boundedness of the trajectory under a condition that is strictly weaker than the standard ones used widely in the literature of continuation methods. Particularly, the often-assumed strictly feasible condition is not required here. When applied to P* complementarity problems, the boundedness of the proposed trajectory turns out to be equivalent to the solvability of the problem, and the entire trajectory converges to the (unique) least element solution provided that it exists. Moreover, for monotone complementarity problems, the whole trajectory always converges to a least 2-norm solution provided that the solution set of the problem is nonempty. The results presented in this paper can serve as a theoretical basis for constructing a new path-following algorithm for solving complementarity problems, even for the situations where the solution set is unbounded.
关键词	complementarity problems continuation methods homotopy continuation trajectories strictly feasible condition P-0-functions P*-functions
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000167548300009
出版者	INST OPERATIONS RESEARCH MANAGEMENT SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16765
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	1.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhao, YB,Li, D. On a new homotopy continuation trajectory for nonlinear complementarity problems[J]. MATHEMATICS OF OPERATIONS RESEARCH,2001,26(1):119-146.
APA	Zhao, YB,&Li, D.(2001).On a new homotopy continuation trajectory for nonlinear complementarity problems.MATHEMATICS OF OPERATIONS RESEARCH,26(1),119-146.
MLA	Zhao, YB,et al."On a new homotopy continuation trajectory for nonlinear complementarity problems".MATHEMATICS OF OPERATIONS RESEARCH 26.1(2001):119-146.