English

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

R2 v1 2026-06-21T17:29:40.726Z