Lifts of Non-Compact Convex Sets and Cone Factorizations

作     者：WANG Chu ZHI Lihong WANG Chu;ZHI Lihong

作者机构：Beijing Jinghang Computation and Communication Research InstituteBeijing 100074China KLMMAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of SciencesBeijing 100049China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2020年第33卷第5期

页      面：1632-1655页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by Equipment Pre-Research Field Fund under Grant Nos.JZX7Y20190258055501,JZX7Y20190243016801 the National Natural Science Foundation of China under Grant No.11901544 the National Key Research Project of China under Grant No.2018YFA0306702 the National Natural Science Foundation of China under Grant No.11571350 supported by National Institute for Mathematical Sciences 2014 Thematic Program on Applied Algebraic Geometry in Daejeon,South Korea 

主　　题：Cone factorization convex set lift nonnegative rank polyhedron positive semidefinite rank recession cone 

摘      要：This paper generalizes the factorization theorem of Gouveia,Parrilo and Thomas to a broader class of convex *** 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 *** 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 *** authors show that the generalized lift of a convex set can also be characterized by the cone factorization of a properly defined slack operator.