Spectrahedral shadows
Optimization and Control
2017-12-05 v3 Algebraic Geometry
Abstract
We show that there are many (compact) convex semi-algebraic sets in euclidean space that do not have a semidefinite representation. This gives a negative answer to a question by Nemirovski, resp. it shows that the Helton-Nie conjecture is false.
Cite
@article{arxiv.1612.07048,
title = {Spectrahedral shadows},
author = {Claus Scheiderer},
journal= {arXiv preprint arXiv:1612.07048},
year = {2017}
}
Comments
ver. 3: changed title, and changed terminology throughout the paper, using "spectrahedral shadows" instead of "sdp representable sets". To appear in SIAGA