Convex Relaxations of Multi-variate Composite Functions

Angelos Tsoukalasa and Alexander Mitsosa, 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, amitsos@alum.mit.edu

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, Fcv and convex and concave relaxations of f, fcv and fcc respectively, McCormick calculates the convex relaxation of g, as

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

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