Perspective envelopes for bilinear functions

We characterize the convex hull of the set defined by a bilinear function f (x, y) = xy and a linear inequality linking x and y. The new characterization, based on perspective functions, dominates the standard McCormick convexification approach. In practice, this result can be of great value in global optimization frameworks, helping to tighten the bounds provided by convex relaxations. The new formulation has the potential to improve the pruning process in spatial branch and bound schemes and consequently reduce the search space effort.