Semidefinite Representation for Convex Hulls of Real Algebraic Curves
Semidefinite Representation for Convex Hulls of Real Algebraic Curves
We show that the closed convex hull of any one-dimensional semialgebraic subset of $\mathbb{R}^n$ is a spectrahedral shadow, meaning that it can be written as a linear image of the solution set of some linear matrix inequality. This is proved by an application of the moment relaxation method. Given a …