23rd European Symposium on Computer Aided Process Engineering

Convex Relaxations of Multi-variate Composite Functions

Angelos Tsoukalas^a and Alexander Mitsos^{a, b},^∗    aDepartment of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, ^bAVT Process Systems Engineering (SVT), RWTH Aachen University, Turmstrasse 46, Aachen, 52064, Germany, Aachen University, [e-mail]

Abstract

McCormick [Math. Progr. 1976] provided the framework for the computation of convex relaxations of composite functions g=F(f(z)) with F a univariate function. Given a convex relaxation of F, F^cv and convex and concave relaxations of f, f^cv and f^cc respectively, McCormick calculates the convex relaxation of g, as

This allows the relaxation of so-called factorable functions. We discuss the construction ...