Characterizing the Inscribability of Polytopes Using Slack Matrices

Abstract

The inscribability of polytopes describes whether polytopes have a realization where all vertices lie on the same sphere. In this work, we characterize the problem of checking the inscribability of polytopes as a min-rank optimization problem based on slack matrices. We provide an SDP relaxation of the problem and prove that it is tight for certain classes of polytopes. For general polytopes, we apply the alternating projection method to the min-rank problem and design numerical experiments to demonstrate its accuracy.

Yiwen Chen

PhD student in Mathematics

My research interests include derivative-free optimization, numerical optimization, and discrete geometry.