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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 
for NMinimize[] reads:

"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

• References:
  • NMinimize Bug in Mathematica 7.0?
    • From: appris@att.net