Title: On representing the positive semidefinite cone using the second-order cone
Abstract:The cone plays an important role in convex optimization and has strong expressive abilities despite its apparent simplicity. Second-order cone formulations can also be solved more efficiently than sem...The cone plays an important role in convex optimization and has strong expressive abilities despite its apparent simplicity. Second-order cone formulations can also be solved more efficiently than semidefinite programming in general. We consider the following question, posed by Lewis and Glineur, Parrilo, Saunderson: is it possible to express the general positive semidefinite cone using cones? We provide a negative answer to this question and show that the 3x3 positive semidefinite cone does not admit any cone representation. Our proof relies on exhibiting a sequence of submatrices of the slack matrix of the 3x3 positive semidefinite cone whose second-order cone rank grows to infinity. We also discuss the possibility of representing certain slices of the 3x3 positive semidefinite cone using the cone.Read More
Publication Year: 2016
Publication Date: 2016-10-16
Language: en
Type: preprint
Access and Citation
Cited By Count: 3
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot