  In this paper, we propose a branch-and-bound algorithm for solving nonconvex
quadratic programming problems with box constraints (BoxQP). Our approach
combines existing tools, such as semidefinite programming (SDP) bounds
strengthened through valid inequalities with a new class of optimality-based
linear cuts which leads to variable fixing. The most important effect of fixing
the value of some variables is the size reduction along the branch-and-bound
tree, allowing to compute bounds by solving SDPs of smaller dimension.
Extensive computational experiments over large dimensional (up to $n=200$) test
instances show that our method is the state-of-the-art solver on large-scale
BoxQPs. Furthermore, we test the proposed approach on the class of binary QP
problems, where it exhibits competitive performance with state-of-the-art
solvers.
