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

• To: mathgroup at smc.vnet.net
• Subject: [mg55786] Re: [mg55765] Re: NMinimize--problem with a min-max problem
• From: "Janos D. Pinter" <jdpinter at hfx.eastlink.ca>
• Date: Wed, 6 Apr 2005 03:11:19 -0400 (EDT)
• References: <d2tfro\$qpe\$1@smc.vnet.net> <200504051010.GAA01071@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```
David and Jens,

in general, one needs to define a closed set for the vars x and y, to
guarantee that the model is well-posed. If one sets e.g. x>=0.0001,
y>=0.0001, then the warnings disappear.

Regards,

Janos D. Pinter
PCS Inc.
Web: www.pinterconsulting.com

At 07:10 AM 4/5/2005, Jens-Peer Kuska wrote:

>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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