Locating the least 2-norm solution of linear programs via a path-following method

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	Locating the least 2-norm solution of linear programs via a path-following method
	Zhao, YB ; Li, D
	2002-04-26
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	12 期号:4 页码:893-912
摘要	A linear program has a unique least 2-norm solution, provided that the linear program has a solution. To locate this solution, most of the existing methods were devised to solve certain equivalent perturbed quadratic programs or unconstrained minimization problems. We provide in this paper a new theory which is different from these traditional methods and is an effective numerical method for seeking the least 2-norm solution of a linear program. The essence of this method is a (interior-point-like) path-following algorithm that traces a newly introduced regularized central path that is fairly different from the central path used in interior-point methods. One distinguishing feature of our method is that it imposes no assumption on the problem. The iterates generated by this algorithm converge to the least 2-norm solution whenever the linear program is solvable; otherwise, the iterates converge to a point which gives a minimal KKT residual when the linear program is unsolvable.
关键词	linear programming path-following algorithm regularized central path least 2-norm solution
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000175810600003
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/17095
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, AMSS, Inst Appl Math, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Zhao, YB,Li, D. Locating the least 2-norm solution of linear programs via a path-following method[J]. SIAM JOURNAL ON OPTIMIZATION,2002,12(4):893-912.
APA	Zhao, YB,&Li, D.(2002).Locating the least 2-norm solution of linear programs via a path-following method.SIAM JOURNAL ON OPTIMIZATION,12(4),893-912.
MLA	Zhao, YB,et al."Locating the least 2-norm solution of linear programs via a path-following method".SIAM JOURNAL ON OPTIMIZATION 12.4(2002):893-912.