Re: Nested optimization teaser

• To: mathgroup at smc.vnet.net
• Subject: [mg46072] Re: Nested optimization teaser
• From: "Joshua A. Solomon" <J.A.Solomon at city.ac.uk>
• Date: Thu, 5 Feb 2004 04:02:52 -0500 (EST)
• References: <bvpas6\$sd1\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thanks to Paul Abbot on another thread, I now know the answer is

In[1]:= egg[in_?NumericQ]:=NMinimize[{(x-in)^2},{{x,-1,1}}][[2,1,2]]

js

On 3/2/04 11:29 pm, in article bvpas6\$sd1\$1 at smc.vnet.net, "Joshua A.
Solomon" <J.A.Solomon at city.ac.uk> wrote:

> Consider the toy identity function egg:
>
> In[1]:= egg[in_]:=NMinimize[{(x-in)^2},{{x,-1,1}}][[2,1,2]]
>
> In[2]:= egg[#]&/@{1,2,3}
> Out[2]:= {1.,2.,3.}
>
> Now then, clearly
>
> In[3]:= NMinimize[(2-a)^2,a]
> Out[3]:= {0.,{a->2.}}
>
> However,
>
> In[4]:= NMinimize[(2-egg[a])^2,a]
> Out[4]:= {9.,{a->0}}
>
> I know why this happens. What I don't know, is how to properly construct a
> nested optimization so this doesn't happen. Specifically, how can I find the
> minimum value (and the parameter values that produce it) of a function that
> depends on the minimum value of another function, which, in turn, depends on
> those same parameters?
>
> js

```

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