Spectrahedra and Convex Hulls of Rank-One Elements
Optimization and Control
2015-01-07 v1 Algebraic Geometry
Abstract
The Helton-Nie Conjecture (HNC) is the proposition that every convex semialgebraic set is a spectrahedral shadow. Here we prove that HNC is equivalent to another propo- sition related to quadratically constrained quadratic programming. Namely, that the convex hull of the rank-one elements of any spectrahedron is a spectrahedral shadow. In the case of compact convex semialgebraic sets, the spectrahedra may be taken to be compact. We illustrate the relationship between spetrahedra and these convex subsets with examples.
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Cite
@article{arxiv.1501.01057,
title = {Spectrahedra and Convex Hulls of Rank-One Elements},
author = {Martin Ames Harrison},
journal= {arXiv preprint arXiv:1501.01057},
year = {2015}
}
Comments
11 pages, 2 images