       Re: Minimize[] Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg76349] Re: Minimize[] Problem
• From: anguzman at ing.uchile.cl
• Date: Sun, 20 May 2007 02:28:24 -0400 (EDT)
• References: <f2mfj4\$mh1\$1@smc.vnet.net> <464F0CB0.4040401@gmail.com>

```Thanks for your answer. You are right, I forgot to mention it, but
I'm using Mathematica 5.2.

How about version 5.2.2 ?

Atte Andres Guzman

Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> ha escrito:

> anguzman at ing.uchile.cl wrote:
>> Hello.
>>
>> Why do I get?
>>
>> In:=
>> Minimize[(x^4-6 x^2+1)^2,{x}]
>> Out=
>> {1,{x->0}}
>>
>> when..
>>
>> In:=
>> (x^4-6 x^2+1)^2/.x->1-Sqrt//Simplify
>> Out=
>>
>>
>> x=0 is actually a local maximum.
>> Any answer will be appreciated.
>>
>> Atte Andres Guzman
>
> I am afraid this may be a bug in version 5.2. Even with a constraint,
> Minimize is unable to find a minimum.
>
> In:=
> \$Version
>
> Out=
> "5.2 for Microsoft Windows (June 20, 2005)"
>
> In:=
> Minimize[(x^4 - 6*x^2 + 1)^2, {x}]
>
> Out=
> {1, {x -> 0}}
>
> In:=
> Simplify[Minimize[{(x^4 - 6*x^2 + 1)^2, x < 0}, {x}]]
>
> Minimize::wksol: Warning: There is no minimum in the region described
> by the constraints; returning a result on the boundary. More...
>
> Out=
> {1, {x -> 0}}
>
> In:=
> Chop[NMinimize[(x^4 - 6*x^2 + 1)^2, {x}]]
>
> Out=
> {0, {x -> -0.41421356237309503}}
>
> In:=
> Chop[N[Solve[(x^4 - 6*x^2 + 1)^2 == 0, x]]]
>
> Out=
> {{x -> -2.414213562373095},
>   {x -> -2.414213562373095},
>   {x -> -0.41421356237309515},
>   {x -> -0.41421356237309515},
>   {x -> 0.41421356237309515},
>   {x -> 0.41421356237309515},
>   {x -> 2.414213562373095}, {x -> 2.414213562373095}}
>
> The behavior of Minimize is correct in version 6.0.
>
> In:= \$Version
>
> Out= "6.0 for Microsoft Windows (32-bit) (April 28, 2007)"
>
> In:= Minimize[(x^4 - 6*x^2 + 1)^2, {x}]
>
> Out= {(1 - 6*(-1 - Sqrt)^2 + (-1 - Sqrt)^4)^2, {x -> -1 -
>     Sqrt}}
>
> In:= Simplify[Minimize[(x^4 - 6*x^2 + 1)^2, {x}]]
>
> Out= {0, {x -> -1 - Sqrt}}
>
> In:= Simplify[Minimize[{(x^4 - 6*x^2 + 1)^2, x > 0}, {x}]]
>
> Out= {0, {x -> -1 + Sqrt}}
>
> Regards,
> Jean-Marc

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