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  • 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.
  • 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. (en)
Title
  • Semidefinite Representation of Convex Hulls of Rational Varieties
  • Semidefinite Representation of Convex Hulls of Rational Varieties (en)
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  • Semidefinite Representation of Convex Hulls of Rational Varieties
  • Semidefinite Representation of Convex Hulls of Rational Varieties (en)
skos:notation
  • RIV/68407700:21230/11:00181653!RIV12-GA0-21230___
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  • P(GAP103/10/0628)
http://linked.open...iv/cisloPeriodika
  • 3
http://linked.open...vai/riv/dodaniDat
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  • Henrion, Didier
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  • 228778
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  • RIV/68407700:21230/11:00181653
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  • Semidefinite programming; Convex optimization; Polynomials; Problems of moments; Rational varieties; Real algebraic geometry (en)
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  • NL - Nizozemsko
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  • [5FC39739EAFB]
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  • Acta Applicandae Mathematicae
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  • 115
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  • Henrion, Didier
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  • 000293285400005
issn
  • 0167-8019
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  • 10.1007/s10440-011-9623-9
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  • 21230
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