A new branch and bound algorithm for noncovex quadratic programming with box constraints

Abstract

In this paper, we investigate a class of nonconvex quadratic programming with box constrains. A new branch and bound algorithm is proposed. The improvement of the new method is how to determine the lower bound. We put nonconvex quadratic programming into convex quadratic programming, and get an optimal solution as lower bound of original problem. Meanwhile, an upper bound is got by existing methods. Moreover, by used of the branch and bound algorithm, we can solve the original problem by solved a series of subproblems. Finally, the convergence of the proposed new algorithm is proved.