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