Lifts of Non-Compact Convex Sets and Cone Factorizations

doi:10.1007/s11424-020-9050-y

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	Lifts of Non-Compact Convex Sets and Cone Factorizations
	Wang, Chu 1; Zhi, Lihong 2,3
	2020-08-04
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
页码	24
摘要	This paper generalizes the factorization theorem of Gouveia, Parrilo and Thomas to a broader class of convex sets. Given a general convex set, the authors define a slack operator associated to the set and its polar according to whether the convex set is full dimensional, whether it is a translated cone and whether it contains lines. The authors strengthen the condition of a cone lift by requiring not only the convex set is the image of an affine slice of a given closed convex cone, but also its recession cone is the image of the linear slice of the closed convex cone. The authors show that the generalized lift of a convex set can also be characterized by the cone factorization of a properly defined slack operator.
关键词	Cone factorization convex set lift nonnegative rank polyhedron positive semidefinite rank recession cone
DOI	10.1007/s11424-020-9050-y
收录类别	SCI
语种	英语
资助项目	Equipment Pre-Research Field Fund[JZX7Y20190258055501] ; Equipment Pre-Research Field Fund[JZX7Y20190243016801] ; National Natural Science Foundation of China[11571350] ; National Natural Science Foundation of China[11901544] ; National Key Research Project of China[2018YFA0306702] ; National Institute for Mathematical Sciences 2014 Thematic Program on Applied Algebraic Geometry in Daejeon, South Korea
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000555391900004
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51913
专题	中国科学院数学与系统科学研究院
通讯作者	Zhi, Lihong
作者单位	1.Beijing Jinghang Computat & Commun Res Inst, Beijing 100074, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Wang, Chu,Zhi, Lihong. Lifts of Non-Compact Convex Sets and Cone Factorizations[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2020:24.
APA	Wang, Chu,&Zhi, Lihong.(2020).Lifts of Non-Compact Convex Sets and Cone Factorizations.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,24.
MLA	Wang, Chu,et al."Lifts of Non-Compact Convex Sets and Cone Factorizations".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY (2020):24.