       Re: optimization nested in root-finding

• To: mathgroup at smc.vnet.net
• Subject: [mg64998] Re: [mg64984] optimization nested in root-finding
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 11 Mar 2006 05:15:33 -0500 (EST)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

```obj2[x_,y_]:=(x-2)^2+(y-3)^2;

f2[x_?NumericQ]:=Module[{y},FindMinimum[obj2[x,y],{y,0}][]];

FindRoot[f2[x]==5,{x,3,5}]

{x -> 4.23606797749979}

Bob Hanlon

>
> From: "E. Neely Atkinson" <eatkinso at mdanderson.org>
To: mathgroup at smc.vnet.net
> Subject: [mg64998] [mg64984] optimization nested in root-finding
>
> I want to find some zeros of a function f(x). The evaluation of
> f in turn requires finding a minimum. For a simple example.
>
> obj2[x_, y_] := (x - 2)^2 + (y - 3)^2
>
> f2[x_] :=
>  Module[
>     {y},
>     FindMinimum[obj2[x, y], {y, 0}][]
>     ]
>
> Thus, f2[x] is the minimum value obj[x,y] can take for a
> given fixed x.
>
> Now, I can plot f2[x] and all is well. However, when
> I try to solve f2[x]==5, I have trouble.
>
> FindRoot[f2[x] == 5, {x, 1, 1.01}]
>
> complains and returns. I am sure I am doing something silly,
> but I am having a slow-brain day and would appreciate any help.
>
> Neely Atkinson
> Department of Biostatistics and Applied Mathematics
> M. D. Anderson Cancer Center
>
> eatkinso at mdanderson.org
>
>

```

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