NEW BRANCH AND BOUND METHOD OVER A BOXED SET OF $\mathbb{R}^{n}$

We present in this paper the new Branch and Bound method with new quadratic approach over a boxed set (a rectangle) of $\mathbb{R}^{n}$. We construct an approximate convex quadratics functions of the objective function to fined a lower bound of the global optimal value of the original non convex quadratic problem (NQP) over each subset of this boxed set. We applied a partition and technical reducing on the domain of (NQP) to accelerate the convergence of the proposed algorithm. Finally,we study the convergence of the proposed algorithm and we give a simple comparison between this method and another methods wish have the same principle.