Re: NMinimize Bug in Mathematica 7.0?

• To: mathgroup at smc.vnet.net
• Subject: [mg96320] Re: NMinimize Bug in Mathematica 7.0?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 11 Feb 2009 05:23:31 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <200902091033.FAA12301@smc.vnet.net> <gmrltf\$9h0\$1@smc.vnet.net>

```In article <gmrltf\$9h0\$1 at smc.vnet.net>,
"Jaccard Florian" <Florian.Jaccard at he-arc.ch> wrote:

> I would avoid to use numerical methods without looking at a graphic.
> As you can see:
> Plot[x - 3*x^2 + x^4,{x, -2, 2}]
>
> Both answers are correct, they give approximations of local minimums.
> You can ask for a minimal and maximal bound for the local minimums like =
> this :
>
> In[8]:= NMinimize[x - 3*x^2 + x^4,{x, -2, -1}]
>
> Out[8]= {-3.513905038934789,
>    {x -> -1.3008395739047898}}
>
> In[9]:= NMinimize[x - 3*x^2 + x^4,{x, 0.5, 1.5}]
>
> Out[9]= {-1.0702301817761541,
>    {x -> 1.1309011226299863}}
>
> If you want the absolute minimum, use a non-numeric method :
>
> In[11]:= N[Minimize[x - 3*x^2 + x^4, x]]
>
> Out[11]= {-3.5139050389347894,{x -> -1.3008395659415772}}

NMinimize[] is designed to find *global* minima. The text cell just
above the input cell of the first example on the online documentation

"Find the global minimum of an unconstrained problem"

Then the following example is given,

In[1]:= NMinimize[x^4 - 3 x^2 + x, x]

Out[1]= {-1.07023, {x -> 1.1309}}

And the result is clearly wrong since it is not a *global* minimum
contrary to what is claimed in this very same documentation.

One should never forget that the Mathematica documentation centre is a
"live" environment, that is, one can re-evaluate the cells (great
feature), which also means that when the documentation for a given
release is generated anew, therefore the new bugs in Mathematica
functions are also carried on in the documentation itself.

Regards,
--Jean-Marc

```

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