Semidefinite Representation of Convex Hulls of Rational Varieties |
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Authors: | Didier Henrion |
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Affiliation: | 1.LAAS,CNRS,Toulouse,France;2.UPS, INSA, INP, ISAE, LAAS,Université de Toulouse,Toulouse,France;3.Faculty of Electrical Engineering,Czech Technical University in Prague,Prague,Czech Republic |
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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. |
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