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Re: NMinimize--problem with a min-max problem


Hi,

fun1[z_?NumericQ] := fun1[z] = NMaximize[{(
Log[x] + 4/3 z Log[
y])/(2 (3/4 + z)), x > 0, y > 0, x + y == 1}, {x, 
y}][[1]]



NMinimize[fun1[z], z]



gives several waring messages, because the result 
of fun1[] is not always a number, but you get a 
result.

Regards

  Jens

"David" <isolanoster at gmail.com> schrieb im 
Newsbeitrag news:d2tfro$qpe$1 at smc.vnet.net...
> Hello,
>
> I'm trying to solve numerically the following 
> problem:
>
> min{z}max{y,x} f{x,y,z}
>
> I first do the maximization:
>
> fun1[z_] := NMaximize[{(
>  Log[x] + 4/3 z Log[
>      y])/(2 (3/4 + z)), x > 0, y > 0, x + y == 
> 1}, {x, y}][[1]]
>
> I can plot fun1[z] (the solution is at 
> z=.75,x=y=1/2) however NMinimize
> does accept the definition of fun1[z] as:
>
> NMinimize[fun1[z], z]
>
> yields error.
>
> Any suggestion?
>
> Thank you in advance,
>
> David
> 



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