Semidefinite representation of convex hulls of rational varieties

Details Semidefinite representation of convex hulls of rational varieties Semidefinite representation of convex hulls of rational varieties

2009-01-13

arxiv.org/abs/0901.1821v3

Mathematics

Optimization and Control

Scientific paper

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.

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