  Quadratically constrained quadratic programs (QCQPs) are a fundamental class
of optimization problems well-known to be NP-hard in general. In this paper we
study sufficient conditions for a convex hull result that immediately implies
that the standard semidefinite program (SDP) relaxation of a QCQP is tight. We
begin by outlining a general framework for proving such sufficient conditions.
Then using this framework, we show that the convex hull result holds whenever
the quadratic eigenvalue multiplicity, a parameter capturing the amount of
symmetry present in a given problem, is large enough. Our results also imply
new sufficient conditions for the tightness (as well as convex hull exactness)
of a second order cone program relaxation of simultaneously diagonalizable
QCQPs.
