Rational parametrization of surfaces
Journal of Symbolic Computation
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Convex sets with semidefinite representation
Mathematical Programming: Series A and B
Rational Algebraic Curves: A Computer Algebra Approach
Rational Algebraic Curves: A Computer Algebra Approach
The algebra and geometry of steiner and other quadratically parametrizable surfaces
Computer Aided Geometric Design
Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets
SIAM Journal on Optimization
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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.