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Re: NMinimize Bug in Mathematica 7.0?

• To: mathgroup at smc.vnet.net
• Subject: [mg96225] Re: [mg96197] NMinimize Bug in Mathematica 7.0?
• From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
• Date: Tue, 10 Feb 2009 05:46:41 -0500 (EST)
• References: <200902091033.FAA12301@smc.vnet.net>

Hello,

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}}


Jaccard Florian




-----Message d'origine-----
De : appris at att.net [mailto:appris at att.net]
Envoy=E9 : lundi, 9. f=E9vrier 2009 11:34
=C0 : mathgroup at smc.vnet.net
Objet : [mg96197] NMinimize Bug in Mathematica 7.0?

Here is an example from Mathematica's user's guide:

In[8]:= NMinimize[x^4 - 3 x^2 + x, x]

Out[8]=  {-3.513905039, {x -> -1.300839566}}

however, trying to replicate it, I get the following:

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

Out[2]= {-1.070230182, {x -> 1.130901122}}

One way to find the global min, I had to use a constraint such as x<0.

Has anyone come across such a problem?

In[3]:= $Version

Out[3]= "7.0 for Microsoft Windows (32-bit) (November 10, 2008)"

Thanks.

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