Lifts of Non-Compact Convex Sets and Cone Factorizations

• 作 者: WANG Chu ZHI Lihong
• 机 构: Beijing Jinghang Computation and Communication Research Institute, Beijing 100074, China;KLMM, Acade
• 出 处: 系统科学与复杂性学报（英文版）
• 发表日期: 2020年5期
• 关键词: Cone factorization convex set lift nonnegative rank polyhedron positive semidefi

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.