  Recently, we proposed a class of inequalities called lifted bilinear cover
inequalities, which are second-order cone representable convex inequalities,
and are valid for a set described by a separable bilinear constraint together
with bounds on variables. In this paper, we study the computational potential
of these inequalities for separable bilinear optimization problems. We first
prove that the semi-definite programming relaxation provides no benefit over
the McCormick relaxation for such problems. We then design a simple randomized
separation heuristic for lifted bilinear cover inequalities. In our
computational experiments, we separate many rounds of these inequalities
starting from McCormick's relaxation of instances where each constraint is a
separable bilinear constraint set. We demonstrate that there is a significant
improvement in the performance of a state-of-the-art global solver in terms of
gap closed, when these inequalities are added at the root node compared to when
they are not.
