Convex Hulls of Quadratically Parameterized Sets With Quadratic Constraints
نویسنده
چکیده
{(f1(x), . . . , fm(x)) : x ∈ T } for quadratic polynomials f0, . . . , fm and a subset T of R . This paper studies semidefinite representation of the convex hull conv(V ) or its closure, i.e., describing conv(V ) by projections of spectrahedra (defined by linear matrix inequalities). When T is defined by a single quadratic constraint, we prove that conv(V ) is equal to the first order moment type semidefinite relaxation of V , up to taking closures. Similar results hold when every fi is a quadratic form and T is defined by two homogeneous (modulo constants) quadratic constraints, or when all fi are quadratic rational functions with a common denominator and T is defined by a single quadratic constraint, under some general conditions.
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