  We consider the global optimization of nonconvex quadratic programs and
mixed-integer quadratic programs. We present a family of convex quadratic
relaxations which are derived by convexifying nonconvex quadratic functions
through perturbations of the quadratic matrix. We investigate the theoretical
properties of these quadratic relaxations and show that they are equivalent to
some particular semidefinite programs. We also introduce novel branching
variable selection strategies which can be used in conjunction with the
quadratic relaxations investigated in this paper. We integrate the proposed
relaxation and branching techniques into the global optimization solver BARON,
and test our implementation by conducting numerical experiments on a large
collection of problems. Results demonstrate that the proposed implementation
leads to very significant reductions in BARON's computational times to solve
the test problems.
