Convex Hulls of Quadratically Parameterized Sets With Quadratic Constraints

Jiawang Nie

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arXiv · 1110.2526

Convex Hulls of Quadratically Parameterized Sets With Quadratic Constraints

Jiawang Nie

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Abstract

Let V be a semialgebraic set parameterized by quadratic polynomials over a quadratic set T. This paper studies semidefinite representation of its convex hull by projections of spectrahedra (defined by linear matrix inequalities). When T is defined by a single quadratic constraint, we prove that its convex hull is equal to the first order moment type semidefinite relaxation of $V$, up to taking closures. Similar results hold when every quadratic polynomial is homogeneous and T is defined by two homogeneous quadratic constraints,or V is defined by rational quadratic parameterizations.

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Jiawang Nie. 2011-10-11. Convex Hulls of Quadratically Parameterized Sets With Quadratic Constraints. https://arxiv.org/abs/1110.2526

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