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MathGroup Archive 2006

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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}][[1]]];

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}][[1]]
>     ]
> 
> 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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