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

• To: mathgroup at smc.vnet.net
• Subject: [mg55765] Re: NMinimize--problem with a min-max problem
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Tue, 5 Apr 2005 06:10:47 -0400 (EDT)
• Organization: Uni Leipzig
• References: <d2tfro\$qpe\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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}][]

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}][]
>
> 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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