Exponential transformation: Difference between revisions
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Author: Daphne Duvivier (dld237), Daniela Gil (dsg254), Jacqueline Jackson (jkj49, Sinclaire Mills (sm2795), Vanessa Nobre (vmn28) Fall 2021 | 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 <ref>{{cite news |last=Boyd |first=Stephen |last2=Kim |first2=Seung-Jean |last3=Vandenberghe |first3=Lieven |last4=Hassibi |first4=Arash |format=PDF |title=A tutorial on geometric programming |work=Springer Science+Business Media, LLC 2007 |publisher=Springer Science+Business Media, LLC 2007 |date=2007-04-10 |deadurl=no |archiveurl=https://web.stanford.edu/~boyd/papers/pdf/gp_tutorial.pdf }}</ref> : | |||
<math> f(x) = \sum_{k=1}^N c_k{x_1}^{a_1k}{x_2}^{a_2k}....{x_n}^{a_nk} </math> | |||
where <math> c_k \geq 0 </math> and <math> x_n \geq0 </math> | |||
A transformation of <math> x_n = e^u_i </math> is applied | |||
Transformed into convex MINLP | |||
<math> | |||
\ln c | |||
</math> | |||
== Proof == | |||
== Numerical Example == | |||
== Applications == | |||
== Conclusion == | |||
Exponential transformation is a powerful method to linearize | |||
== References == | |||
<references /> | |||
Revision as of 14:04, 27 November 2021
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] :
where and
A transformation of is applied
Transformed into convex MINLP
Proof
Numerical Example
Applications
Conclusion
Exponential transformation is a powerful method to linearize