2011-09-01, English, Article, Report edition: Semidefinite Representation of Convex Hulls of Rational Varieties.(Report) Henrion, Didier

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Physical Description
  • Report
  • Magazine/​Journal article
Published
  • Springer, 2011 Sept
Language
  • English

Edition details

Title
  • Semidefinite Representation of Convex Hulls of Rational Varieties.(Report)
Also Titled
  • Semidefinite Representation of Convex Hulls of Rational Varieties.
Appears In
  • Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications, v.115, no.3, 2011 Sept, p.319(9) (ISSN: 0167-8019)
Author
  • Henrion, Didier
Published
  • Springer, 2011 Sept
Physical Description
  • Report
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • Byline: Didier Henrion (1,2,3) Keywords: Semidefinite programming; Convex optimization; Polynomials; Problems of moments; Rational varieties; Real algebraic geometry 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. Author Affiliation: (1) LAAS, CNRS, 7 avenue du colonel Roche, 31077, Toulouse, France (2) UPS, INSA, INP, ISAE, LAAS, Universite de Toulouse, 31077, Toulouse, France (3) Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, 16626, Prague, Czech Republic Article History: Registration Date: 07/​06/​2011 Received Date: 24/​03/​2010 Accepted Date: 06/​06/​2011 Online Date: 17/​06/​2011 Article note: This work was partly supported by research project 103/​10/​0628 of the Grant Agency of the Czech Republic.
Terms of Use
  • COPYRIGHT 2011 Springer
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 262785428

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