Deciding polyhedrality of spectrahedra
Optimization and Control
2015-07-22 v3 Metric Geometry
Abstract
Spectrahedra are linear sections of the cone of positive semidefinite matrices that, as convex bodies, generalize the class of polyhedra. In this paper we investigate the problem of recognizing when a spectrahedron is polyhedral. We reprove a result of Ramana (1998) regarding the structure of spectrahedra and we devise a normal form of representations of spectrahedra. This normal form is effectively computable and leads to an algorithm for deciding polyhedrality.
Keywords
Cite
@article{arxiv.1102.4367,
title = {Deciding polyhedrality of spectrahedra},
author = {Avinash Bhardwaj and Philipp Rostalski and Raman Sanyal},
journal= {arXiv preprint arXiv:1102.4367},
year = {2015}
}
Comments
12 pages, 3 figures; v3: minor improvements; SIAM J. Opt, accepted for publication