Exploiting vector space properties to strengthen the relaxation of bilinear programs arising in the global optimization of process networks

In this paper we present a methodology for finding tight convex relaxations for a special set of quadratic constraints given by bilinear and linear terms that frequently arise in the optimization of process networks. The basic idea lies on exploiting the interaction between the vector spaces where the different set of variables are defined in order to generate cuts that will tighten the relaxation of traditional approaches. These cuts are not dominated by the McCormick convex envelopes and can be effectively used in conjunction with them. The performance of the method is tested in several case studies by implementing the resulting relaxation within a spatial branch and bound framework.