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

Fix and Bound: An efficient approach for solving large-scale quadratic programming problems with box constraints