A new rectangle branch-and-reduce approach for solving nonconvex quadratic programming problems

The paper presents a new rectangle branch-and-reduce approach for solving nonconvex quadratic programming problems, in which a new lower approximate linear functions of the quadratic function over an n-rectangle is given to determine a lower bound of the global optimal value of the original problem over each rectangle, and a simple two-partition technique on rectangle is used, as well as the tactics on reducing and deleting subrectangles is used to accelerate the convergence of the proposed algorithm. The proposed algorithm is proved to be convergent and shown to be effective with numerical results.