A ROBUST INTERIOR POINT METHOD FOR COMPUTING THE ANALYTIC CENTER OF AN ILL-CONDITIONED POLYTOPE WITH ERRORS

doi:10.4208/jcm.1907-m2019-0016

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	A ROBUST INTERIOR POINT METHOD FOR COMPUTING THE ANALYTIC CENTER OF AN ILL-CONDITIONED POLYTOPE WITH ERRORS
	Wang, Zhouhong 1; Dai, Yuhong 2,3; Xu, Fengmin 4
	2019
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	37 期号:6 页码:843-865
摘要	In this paper we propose an efficient and robust method for computing the analytic center of the polyhedral set P = {x is an element of R-n vertical bar Ax = b; x >= 0}, where the matrix A is an element of R-mxn is ill-conditioned, and there are errors in A and b. Besides overcoming the difficulties caused by ill-conditioning of the matrix A and errors in A and b, our method can also detect the infeasibility and the unboundedness of the polyhedral set P automatically during the computation. Detailed mathematical analyses for our method are presented and the worst case complexity of the algorithm is also given. Finally some numerical results are presented to show the robustness and effectiveness of the new method.
关键词	Analytic center Ill-conditioning Unboundedness Primal-dual interior point algorithm Convergence Polynomial complexity
DOI	10.4208/jcm.1907-m2019-0016
收录类别	SCI
语种	英语
资助项目	Chinese Natural Science Foundation[11631013] ; Chinese Natural Science Foundation[71331001] ; Chinese Natural Science Foundation[11331012] ; National 973 Program of China[2015CB856002] ; Chinese NSF[11631013] ; Chinese NSF[11571271] ; Chinese NSF[11605139]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000504738100006
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50474
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Zhouhong
作者单位	1.Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LESC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Xi An Jiao Tong Univ, Sch Econ & Finance, Xian 710061, Shaanxi, Peoples R China
推荐引用方式 GB/T 7714	Wang, Zhouhong,Dai, Yuhong,Xu, Fengmin. A ROBUST INTERIOR POINT METHOD FOR COMPUTING THE ANALYTIC CENTER OF AN ILL-CONDITIONED POLYTOPE WITH ERRORS[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2019,37(6):843-865.
APA	Wang, Zhouhong,Dai, Yuhong,&Xu, Fengmin.(2019).A ROBUST INTERIOR POINT METHOD FOR COMPUTING THE ANALYTIC CENTER OF AN ILL-CONDITIONED POLYTOPE WITH ERRORS.JOURNAL OF COMPUTATIONAL MATHEMATICS,37(6),843-865.
MLA	Wang, Zhouhong,et al."A ROBUST INTERIOR POINT METHOD FOR COMPUTING THE ANALYTIC CENTER OF AN ILL-CONDITIONED POLYTOPE WITH ERRORS".JOURNAL OF COMPUTATIONAL MATHEMATICS 37.6(2019):843-865.