Semidefinite Representation of Convex Hulls of Rational Varieties
Semidefinite Representation of Convex Hulls of Rational Varieties
复制标题
DOI：
10.1007/s10440-011-9623-9
复制
发表时间：
2009-01
影响因子：
1.6
通讯作者：
D. Henrion
中科院分区：
文献类型：
--
作者：
D. Henrion
利用半正定矩矩阵的初等对偶性质和多项式平方和分解，证明了有理参数化代数簇的凸船体是半定可表示的（也就是说，它可以表示为半正定矩阵锥的仿射截面的投影）的情况下（a）曲线;（B）超曲面参数化的二次;和（c）由二元四次曲线参数化的超曲面;所有这些超曲面都在任意维的环境空间中。
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.