Didier Henrion
Published 2009-01-13, updated 2011-01-28Version 3
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.
Spectrahedra and Convex Hulls of Rank-One Elements
A Note on the Convex Hull of Finitely Many Projections of Spectrahedra
Estimating the convex hull of the image of a set with smooth boundary: error bounds and applications
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