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Re: Symbolic Optimization Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88525] Re: Symbolic Optimization Problem
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 7 May 2008 07:09:31 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fvpd5c$mr4$1@smc.vnet.net>

Gonca Senel wrote:

> I need to maximize
> 
> \[Pi] = R*\[Alpha] (1/\[Alpha] (\[Beta]/R)^(1/(
==!!!!!
Although it looks nice in the front end, tt is a very bad idea indeed to 
use the Creek symbol pi here, i.e. on the left hand side of an 
assignment, since this symbol has already a built in meaning (and is 
protected against modification:" you will get an error message if you 
evaluate the above expression: Set::wrsym: Symbol \[Pi] is Protected...")

> 1 - \[Beta])) - (1 - \[Gamma])*\[Beta]^(2/(
> 1 - \[Beta]))*\[Alpha]^(\[Beta]/(
> 1 - \[Beta]))) - (1/\[Alpha] (\[Beta]/R)^(1/(
> 1 - \[Beta])) - (1 - \[Gamma])*\[Beta]^(2/(
> 1 - \[Beta]))*\[Alpha]^(\[Beta]/(1 - \[Beta])))
> 
> with respect to R (R will be in terms of alpha, beta and gamma) under the
> assumption that beta, alpha and gamma will all be between 0 and 1. How can
> I solve this symbolic optimization with Mathematica? I tried to solve it
> but I am not very experienced with Mathematica and your help is greatly
> appreciated.

To get a symbolic answer, you should try *Maximize[]*, though I strongly 
doubt that you will be able to get a symbolic answer out of the box for 
your expression.

f = R*\[Alpha] (1/\[Alpha] (\[Beta]/
          R)^(1/(1 - \[Beta])) - (1 - \[Gamma])*\[Beta]^(2/(1 - \
\[Beta]))*\[Alpha]^(\[Beta]/(1 - \[Beta]))) - (1/\[Alpha] (\[Beta]/
         R)^(1/(1 - \[Beta])) - (1 - \[Gamma])*\[Beta]^(2/(1 - \
\[Beta]))*\[Alpha]^(\[Beta]/(1 - \[Beta])))

Maximize[{f, 0 < \[Alpha] < 1, 0 < \[Beta] < 1, 0 < \[Gamma] < 1}, R]

[returned unevaluated]

You should experiment with some numeric values first, just to get a feel 
of what is going on; then you should try to simplify the expression by 
"eliminating" some of the parameters, grouping them into some more 
linear/polynomial forms.

Regards,
-- Jean-Marc


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