  In this paper we show that a convexifiability property of nonconvex quadratic
programs with nonnegative variables and quadratic constraints guarantees zero
duality gap between the quadratic programs and their semi-Lagrangian duals.
More importantly, we establish that this convexifiability is hidden in classes
of nonnegative homogeneous quadratic programs and discrete quadratic programs,
such as mixed integer quadratic programs, revealing zero duality gaps. As an
application, we prove that robust counterparts of uncertain mixed integer
quadratic programs with objective data uncertainty enjoy zero duality gaps
under suitable conditions. Various sufficient conditions for convexifiability
are also given.
