Lifts of Non-Compact Convex Sets and Cone Factorizations  

作　　者：WANG Chu ZHI Lihong 

机构地区：[1]Beijing Jinghang Computation and Communication Research Institute,Beijing 100074,China [2]KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Journal of Systems Science & Complexity》2020年第5期1632-1655,共24页系统科学与复杂性学报（英文版）

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。

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 

分 类 号：O221.1[理学—运筹学与控制论]