  Mixed-integer quadratic programming is the problem of optimizing a quadratic
function over points in a polyhedral set where some of the components are
restricted to be integral. In this paper, we prove that the decision version of
mixed-integer quadratic programming is in NP, thereby showing that it is
NP-complete. This is established by showing that if the decision version of
mixed-integer quadratic programming is feasible, then there exists a solution
of polynomial size. This result generalizes and unifies classical results that
quadratic programming is in NP and integer linear programming is in NP.
