Convex reformulations of mixed-integer quadratically constrained programs

We present a solution approach for the general problem (QP) of minimizing a quadratic function of integer variables subject to a set of quadratic constraints. The resolution is divided into two phases. The ?rst phase is to reformulate the initial problem as an equivalent quadratic problem which continuous relaxation is convex; the second phase is to solve the reformulated problem by a branch and bound algorithm. We further extend these results to the mixed-integer case. Finally, we present some computational experiments on pure-integer and mixed-integer instances of (QP ).