       Re: Re: weird NMaximize behaviour

• To: mathgroup at smc.vnet.net
• Subject: [mg92091] Re: [mg92071] Re: weird NMaximize behaviour
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 20 Sep 2008 04:55:59 -0400 (EDT)
• References: <gat9qm\$ejo\$1@smc.vnet.net> <200809190916.FAA15056@smc.vnet.net>

```I don't think the answer can be as simple as that. Note that:

Table[First[NMaximize[{(x - i)^2, -2 <= x <= 2}, {x}]] -
First[NMaximize[{(x - i)^2, -2 <= x <= 2 && -1 <= y <= 1}, {x,
y}]], {i, 0,
10}]
{0., 8., 0., 0., 0., 0., 0., 0., 0., 0., 0.}

Andrzej Kozlowski

On 19 Sep 2008, at 18:16, dh wrote:

>
>
> Hi Andrzej,
>
> We do not know what method is chosen by the default Method-
> >"Automatic",
>
> but it seems to me that some "up hill" method is invoked. Starting at
>
> some point x0>1, the algorithm will then go towards larger x until
>
> reaching the border of the region.
>
> To fix this, we need to choose a method that does not simply go uphill
>
> but tries to find a global maximum, e.g. "SimulatedAnnealing" or
>
> "DifferentialEvolution". E.g. "SimulatedAnnealing"  gives:
>
> {9.,{x->-2.,y->0.999067}}
>
> Daniel
>
>
>
>
>
> Andrzej Kozlowski wrote:
>
>> I have just encountered strange behaviour by NMaximize (which has
>> been
>
>> ruining a demonstration I have been working on):
>
>>
>
>> This is fine:
>
>>
>
>> NMaximize[{(x - 1)^2, -2 <= x <= 2}, {x}]
>
>> {9., {x -> -2.}}
>
>>
>
>> but this definitely is not:
>
>>
>
>> NMaximize[{(x - 1)^2, -2 <= x <= 2 && -1 <= y <= 1}, {x, y}]
>
>> {1., {x -> 2., y -> 0.87904}}
>
>>
>
>> The objective function s independent of y, yet NMaximize seems to go
>
>> off on some wild goose chase and ends up with a very poor "maximum".
>
>>
>
>> This does not happen here:
>
>>
>
>> NMaximize[{(x - 2)^2, -2 <= x <= 2}, {x}]
>
>> {16., {x -> -2.}}
>
>>
>
>> NMaximize[{(x - 2)^2, -2 <= x <= 2 && -1 <= y <= 1}, {x, y}]
>
>> {16., {x -> -2., y -> -0.980305}}
>
>>
>
>> Kind of weird.
>
>>
>
>> Andrzej Kozlowski
>
>>
>
>
>
>
>
> --
>
>
>
> Daniel Huber
>
> Metrohm Ltd.
>
> Oberdorfstr. 68
>
> CH-9100 Herisau
>
> Tel. +41 71 353 8585, Fax +41 71 353 8907
>
> E-Mail:<mailto:dh at metrohm.com>
>
> Internet:<http://www.metrohm.com>
>
>
>

```

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