Exponential transformation

Author: Daphne Duvivier (dld237), Daniela Gil (dsg254), Jacqueline Jackson (jkj49, Sinclaire Mills (sm2795), Vanessa Nobre (vmn28) Fall 2021

Introduction

Exponential transformations are used for convexification of geometric programming constraints (posynominal) nonconvex optimization problems.

Geometric Programming

Theory & Methodology

Exponential transformation begins with a posynominal noncovex function of the form  :

$f(x)=\sum _{k=1}^{N}c_{k}{x_{1}}^{a_{1}k}{x_{2}}^{a_{2}k}....{x_{n}}^{a_{n}k}$

where $c_{k}\geq 0$ and $x_{n}\geq 0$

A transformation of $x_{n}=e_{i}^{u}$ is applied

Transformed into convex MINLP

$\ln c$

Conclusion

Exponential transformation is a powerful method to linearize