Convex hull results on quadratic programs with non-intersecting constraints

Let F subset of R-n be a nonempty closed set. Understanding the structure of the closed convex hull (C) over bar (F) := <(conv{over bar>{( x, xx(T))|x is an element of F} in the lifted space is crucial for solving quadratic programs related to F. This paper discusses the relationship between C(F) and (C) over bar (G), where G results by adding non-intersecting quadratic constraints to F. We prove that C(G) can be represented as the intersection of C(F) and half spaces defined by the added constraints. The proof relies on a complete description of the asymptotic cones of sets defined by a single quadratic equality and a partial characterization of the recession cone of C(G). Our proof generalizes an existing result for bounded quadratically defined F with non-intersecting hollows and several results on C(G) for G defined by non-intersecting quadratic constraints. The result also implies a sufficient condition for when the lifted closed convex hull of an intersection equals the intersection of the lifted closed convex hulls.