  Mixed integer quadratic programming (MIQP) is the problem of minimizing a
convex quadratic function over mixed integer points in a rational polyhedron.
This paper focuses on the augmented Lagrangian dual (ALD) for MIQP. ALD
augments the usual Lagrangian dual with a weighted nonlinear penalty on the
dualized constraints. We first prove that ALD will reach a zero duality gap
asymptotically as the weight on the penalty goes to infinity under some mild
conditions on the penalty function. We next show that a finite penalty weight
is enough for a zero gap when we use any norm as the penalty function. Finally,
we prove a polynomially bound on the weight on the penalty term to obtain a
zero gap.
