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Semidefinite Representation of Convex Hulls of Rational Varieties

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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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Authors and Affiliations

  1. LAAS, CNRS, 7 avenue du colonel Roche, 31077, Toulouse, France

    Didier Henrion

  2. UPS, INSA, INP, ISAE, LAAS, Université de Toulouse, 31077, Toulouse, France

    Didier Henrion

  3. Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 16626, Prague, Czech Republic

    Didier Henrion

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  1. Didier Henrion
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Correspondence to Didier Henrion.

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This work was partly supported by research project 103/10/0628 of the Grant Agency of the Czech Republic.

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Henrion, D. Semidefinite Representation of Convex Hulls of Rational Varieties. Acta Appl Math 115, 319–327 (2011). https://doi.org/10.1007/s10440-011-9623-9

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  • DOI: https://doi.org/10.1007/s10440-011-9623-9

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