Using convex nonlinear relaxations in the global optimization of nonconvex generalized disjunctive programs

In this paper we present a framework to generate tight convex relaxations for nonconvex generalized disjunctive programs. The proposed methodology builds on our recent work on bilinear and concave generalized disjunctive programs for which tight linear relaxations can be generated, and extends its application to nonlinear relaxations. This is particularly important for those cases in which the convex envelopes of the nonconvex functions arising in the formulations are nonlinear (e.g. linear fractional terms). This extension is now possible by using the latest developments in disjunctive convex programming. We test the performance of the method in three typical process systems engineering problems, namely, the optimization of process networks, reactor networks and heat exchanger networks.