Branch and bound method to resolve non convex quadratic problems over a rectangle of Rn

Abstract

We present in this paper a new convergence of the Branch and Bound method to resolve a class of non convex quadratic problems over a rectangle of Rⁿ . We construct an approximate convex quadratics functions of the objective function in order to determinate the lower bound of the global optimal value of the original problem (NQP) over each subset of the feasible domain of the optimization problem. We applied the partition and reduction technical on the feasable domain to accelerate the convergence of the proposed algorithm. Finally, we give a simple comparison between this method and another method wish has the same principle with examples.