Lifts of Non-Compact Convex Sets and Cone Factorizations
文献类型：期刊论文
| 作者 | Wang, Chu3; Zhi, Lihong1,2 |
| 刊名 | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| 出版日期 | 2020-08-04 |
| 页码 | 24 |
| 关键词 | Cone factorization convex set lift nonnegative rank polyhedron positive semidefinite rank recession cone |
| ISSN号 | 1009-6124 |
| DOI | 10.1007/s11424-020-9050-y |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000555391900004 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51912]  |
| 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.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Beijing Jinghang Computat & Commun Res Inst, Beijing 100074, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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