Difference between revisions of "Exponential transformation"

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Before discussing methods to solve posynomial optimization problems, a brief review of posynomials is of use. A posynomial, as defined by Duffin, Peterson, and Zener (1967) as a function of the form
 
Before discussing methods to solve posynomial optimization problems, a brief review of posynomials is of use. A posynomial, as defined by Duffin, Peterson, and Zener (1967) as a function of the form
  
<math>f(x1,x2,...,xn)=\sum_{k=1}^K c_{\text{k}}x_{\text{1}}^a_{\text{1k}}..x_{\text{n}}^a{\text{nk}}</math>
+
<math>f(x1,x2,...,xn)=sum_{k=1}^K c_{\text{k}}x_{\text{1}}^a_{\text{1k}}..x_{\text{n}}^a{\text{nk}}</math>
 
===Original Development===
 
===Original Development===
 
Content under subtitle 1.1.
 
Content under subtitle 1.1.

Revision as of 13:07, 25 May 2014

Author: Daniel Garcia (ChBE 345)

Stewards: Dajun Yue and Prof. Fengqi You

Date presented: May 25, 2014

This article concerns the exponential transformation method for globally solving posynomial (or general geometric/signomial) optimization problems with nonconvex objective functions or constraints. A discussion of the method's development, use, and limitations will be presented.

Contents

History and Background

Before discussing methods to solve posynomial optimization problems, a brief review of posynomials is of use. A posynomial, as defined by Duffin, Peterson, and Zener (1967) as a function of the form

Failed to parse(PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): f(x1,x2,...,xn)=sum_{k=1}^K c_{\text{k}}x_{\text{1}}^a_{\text{1k}}..x_{\text{n}}^a{\text{nk}}

Original Development

Content under subtitle 1.1.

Historical Use

Give some examples here.

Limitations

Discuss limitations here

Conclusions

Content under conclusions S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}