Upper and lower bounds in quadratic maximization with integer constraints

In this paper the problem or maximizing a quadratic function defined in {-l, l}^n is considered. We propose a technique to obtain an upper bound and a lower bound to the maximum of a quadratic function on the set {-l, l}^n and a feasible point where the lower bound is attained. The problem of the approximability of the quadratic maximization problem with integer constraints by the method proposed here is studied and solved negatively. oreover a special class of matrices such that the feasible point obtained with our method is the solution or the maximization problem considered is given. Numerical implementation of the method proposed and related numerical experience are shown