Semidefinite representation of convex hulls of rational varieties
Optimization and Control
2011-01-31 v3 Systems and Control
Algebraic Geometry
Abstract
Using elementary duality properties of positive semidefinite moment matrices and polynomial sum-of-squares decompositions, we prove that the convex hull of rationally parameterized algebraic varieties is semidefinite representable (that is, it can be represented as a projection of an affine section of the cone of positive semidefinite matrices) in the case of (a) curves; (b) hypersurfaces parameterized by quadratics; and (c) hypersurfaces parameterized by bivariate quartics; all in an ambient space of arbitrary dimension.
Keywords
Cite
@article{arxiv.0901.1821,
title = {Semidefinite representation of convex hulls of rational varieties},
author = {Didier Henrion},
journal= {arXiv preprint arXiv:0901.1821},
year = {2011}
}