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Re: weird NMaximize behaviour
*To*: mathgroup at smc.vnet.net
*Subject*: [mg92162] Re: weird NMaximize behaviour
*From*: dh <dh at metrohm.ch>
*Date*: Mon, 22 Sep 2008 05:25:45 -0400 (EDT)
*References*: <gat9qm$ejo$1@smc.vnet.net> <200809190916.FAA15056@smc.vnet.net> <gb2dra$bct$1@smc.vnet.net>
Hi Andrzej,
I agree, Mathematica must have some mean to decide on which side of the minimum
the largest value, compatible with the conditions, lies.
Daniel
I interprete your example like:
For NMaximize[{(x - i)^2, -2 <= x <= 2}, {x}] the starting value for the
uphill search is taken somwhere between 0..1
Andrzej Kozlowski wrote:
> 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>
>>
>>
>>
>
>
--
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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