@article{LocatelliPiccialliSudoso2024,
  author    = {Locatelli, Marco and Piccialli, Veronica and Sudoso, Antonio M.},
  title     = {Fix and bound: an efficient approach for solving large-scale quadratic programming problems with box constraints},
  journal   = {Mathematical Programming Computation},
  volume    = {17},
  number    = {2},
  publisher = {Springer Science and Business Media LLC},
  issn      = {1867-2949},
  doi       = {10.1007/s12532-024-00270-y},
  pages     = {231 -- 263},
  year      = {2024},
  abstract  = {In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach com- bines 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.},
  language  = {en}
}