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Re: Points sampled by FindMinimum


On 11/8/06 at 6:06 AM, andrew.j.moylan at gmail.com (Andrew Moylan)
wrote:

>Please consider the following code, which asks FindMinimum to
>minimise a simple parabolic function while tracking at which which
>points FindMinimum evaluates the function:

>func[x_?NumericQ] := (Print[x]; 1 + (x - 1)^2) FindMinimum[func[x],
>{x, 0.1}]

>The output is:

>0.1 0.1 0.1 0.6 0.6 0.6 1. 1. 1. 1. 1. 1.

>But I would have expected output more like:

>0.1 0.6 1. 1.

>Can anyone explain why FindMinimum evaluates func three times at
>each test point, instead of once?

I rather doubt FindMinimum is evaluating the function three 
times at each point. I am reasonably certain the difference 
between sampled points is simply fairly small and the Print 
statement doesn't show enough digits to make it apparent there 
is a difference.

That is

In[4]:=
.1000001

Out[4]=
0.1

In[5]:=
.1000002

Out[5]=
0.1
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