Lifts of Non-Compact Convex Sets and Cone Factorizations
Wang, Chu1; Zhi, Lihong2,3
AbstractThis 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.
KeywordCone factorization convex set lift nonnegative rank polyhedron positive semidefinite rank recession cone
Indexed BySCI
Funding ProjectEquipment 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 Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000555391900004
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Document Type期刊论文
Corresponding AuthorZhi, Lihong
Affiliation1.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
Recommended Citation
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.
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