KMS Of Academy of mathematics and systems sciences, CAS
| Lifts of Non-Compact Convex Sets and Cone Factorizations | |
| Wang, Chu1; Zhi, Lihong2,3 | |
| 2020-08-04 | |
| Source Publication | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| ISSN | 1009-6124 |
| Pages | 24 |
| Abstract | 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. |
| Keyword | Cone factorization convex set lift nonnegative rank polyhedron positive semidefinite rank recession cone |
| DOI | 10.1007/s11424-020-9050-y |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Interdisciplinary Applications |
| WOS ID | WOS:000555391900004 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51913 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zhi, Lihong |
| Affiliation | 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 |
| 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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