On the separation of split inequalities for non-convex quadratic integer programming

We investigate the computational potential of split inequalities for non-convex quadratic integer programming, first introduced by Letchford [11] and further examined by Burer and Letchford [8]. These inequalities can be separated by solving convex quadratic integer minimization problems. For small instances with box-constraints, we show that the resulting dual bounds are very tight; they can close a large percentage of the gap left open by both the RLTand the SDP-relaxations of the problem. The gap can be further decreased by separating so-called non-standard split inequalities, which we examine in the case of ternary variables.