On the tightness of SDP relaxations of QCQPs

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 conditions under which the standard semidefinite program (SDP) relaxation QCQP is tight. We begin by outlining general framework for proving such sufficient conditions. Then using framework, show that SDP tight whenever eigenvalue multiplicity, parameter capturing amount symmetry present given problem, large enough. similar projected epigraph gives convex hull original QCQP. Our results also imply new tightness (as well as exactness) second order cone simultaneously diagonalizable QCQPs.