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Re: Possible simple bug in NMaximize

• To: mathgroup at smc.vnet.net
• Subject: [mg71086] Re: [mg71040] Possible simple bug in NMaximize
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 8 Nov 2006 06:06:12 -0500 (EST)
• References: <200611060752.CAA08685@smc.vnet.net> <385666A3-8452-4267-9A16-51F52DC79904@mimuw.edu.pl>

On 6 Nov 2006, at 19:05, Andrzej Kozlowski wrote:

>
> On 6 Nov 2006, at 16:52, Nick Grishin wrote:
>
>> (* does not work *)
>> func = Hold[NIntegrate[t^3, {t, x, 0}]];
>> NMaximize[func, x]
>>
>> (* works *)
>> func = Hold[NIntegrate[t^3, {t, 0, x}]];
>> NMinimize[func, x]
>>
>> $Version
>> 5.2 for Microsoft Windows (June 20, 2005)
>>
>
> A bug in NMaximize? Why? It behaves exactly as it should do with  
> this kind of input.  The problem is with MMinimize, because you  
> when you give it nonsensical input it actually produces output,  
> which unfortunately (by sheer accident),  looks as if it might be  
> right. But it is nonssense nonetheless (nonsense in - > nonsense  
> out) nonsensical, and  to convince you of it I will slightly change  
> your input:
>
> func = Hold[NIntegrate[t^3, {t, 10, x}]];
>
>
> NMinimize[func, x]
>
>
> {-2500.0000000000005, {x -> -0.0002833987269403981}}
>
> Now, does this look like it "works"?
>
> Andrzej Kozlowski


One correct way to do this kind of thing would be:

func [x_?NumericQ] := NIntegrate[t^3, {t, 0, x}]

Then


Chop[NMinimize[func[x], x]]


{0, {x -> -8.478781415049459*^-9}}

and

NMaximize[func[x], x]
NMaximize::"cvdiv" : "Failed to converge to a solution. The function  
may be unbounded.

{8.16355648507784698932167375`15.954589770191005*^537, {x ->  
-4.250938758824719*^134}}


both of which at least make sense.

Andrzej Kozlowski
Tokyo, Japan

• References:
  • Possible simple bug in NMaximize
    • From: Nick Grishin <grishin@chop.swmed.edu>