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 [1] :
$ f(x) = \sum_{k=1}^N c_k{x_1}^{a_1k}{x_2}^{a_2k}....{x_n}^{a_nk} $
where $ c_k \geq 0 $ and $ x_n \geq0 $
A transformation of $ x_n = e^u_i $ is applied
Transformed into convex MINLP
$ \ln c $
Proof
Numerical Example
Applications
Conclusion
Exponential transformation is a powerful method to linearize