       Re: weird NMaximize behaviour

• To: mathgroup at smc.vnet.net
• Subject: [mg92071] Re: weird NMaximize behaviour
• From: dh <dh at metrohm.ch>
• Date: Fri, 19 Sep 2008 05:16:09 -0400 (EDT)
• References: <gat9qm\$ejo\$1@smc.vnet.net>

```
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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