Re: NMinimize--problem with a min-max problem
- To: mathgroup at smc.vnet.net
- Subject: [mg55804] Re: [mg55753] NMinimize--problem with a min-max problem
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Wed, 6 Apr 2005 03:12:05 -0400 (EDT)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
expr=(Log[x]+4/3 z Log[1-x])/(2 (3/4+z));
solnx=Solve[D[expr,x]==0,x][[1]]
{x -> 3/(4*z + 3)}
solnz=Solve[D[expr/.solnx,z]==0,z][[1]]
{z -> 3/4}
solnx=solnx/.solnz
{x -> 1/2}
expr/.solnx/.solnz
-((2*Log[2])/3)
%//N
-0.46209812037329684
Clear[fun1];
fun1[z_?NumericQ] :=
NMaximize[{(Log[x]+4/3 z Log[1-x])/(2 (3/4+z)),
0<x<1},{x}][[1]];
Off[NMaximize::nnum];
NMinimize[fun1[z],z]
{-0.4620981203732968, {z -> 0.7499999786528403}}
Bob Hanlon
>
> From: "David" <isolanoster at gmail.com>
To: mathgroup at smc.vnet.net
> Date: 2005/04/05 Tue AM 03:21:55 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg55804] [mg55753] NMinimize--problem with a min-max problem
>
> 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
>
>