A novel branch-and-bound algorithm for quadratic mixed-integer problems with quadratic constraints

The efficient numerical treatment of convex quadratic mixed-integer optimization poses a challenging problem for present branch-and-bound algorithms. We introduce a method based on the duality principle for nonlinear convex problems to derive suitable bounds that can be directly exploit to improve heuristic branching rules. Numerical results indicate that the bounds allow the branch-and-bound tree to be searched and evaluated more efficiently compared to benchmark solvers. An extended computational study using different performance measures is presented for small, medium and large test instances. AMS Classification: 90C11, 90C20