2014/12/31 by Chu Wang, Wang, Chu, Lihong Zhi +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1501.00115
openalex publication_date 2014/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we generalize the factorization theorem of Gouveia, Parrilo and Thomas to a broader class of convex sets. Given a general convex set, we 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. We 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. We show that the generalized lift of a convex set can also be characterized by the cone factorization of a properly defined slack operator.