       Re: Two successive FindMinimum -> Bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg74352] Re: Two successive FindMinimum -> Bug?
• From: Peter Pein <petsie at dordos.net>
• Date: Mon, 19 Mar 2007 02:09:09 -0500 (EST)
• References: <etik3j\$j32\$1@smc.vnet.net>

```Dmitry Garanin schrieb:
> Hi All,
>
> I am trying to solve a problem that requires application of FindMinimum (or similar rutines two times and it does not work. Here is a simplified example:
>
>
> fxt[x_,t_]=(x^2-t)^2  (* Searching for a minimal t for which fxt turns to zero *)
> tminx[x_]:=t/.FindMinimum[fxt[x,t],{t,1}][] (* Finding the minimizing t for a given x *)
> tminabs=FindMinimum[tminx[x],{x,1}]  (* Minimizing this t with respect to x. The result should be tminabs=0 at x=0 *)
>
> The last command here does not work since, evidently tminx[x] (that is x^2 for us humans) is not treated as a regular function.
>
> Is there a bug here or I am doing something wrong??
>
> Help is appreciated.
>
>
> http://profiles.yahoo.com/dgaranin
>

Hi Dmitry,

either define tmin as a function of numerical arguments:

tmin[x_?NumericQ]:=...

or (for simple functions fxt)

tmin[x_]:=
t /. ToRules[Reduce[D[fxt[x,t],t] == 0 && D[fxt[x,t], {t,2}] > 0, t]]

hth,
Peter

```

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