I'm not sure why you recommended minimizing z^2, as opposed to just z.
If, for example, z12 = f(1,2) = 5 and z41 = f(4,1) = 2, then z12^2 = 25
and z41^2 = 4, thus giving z41 as the minimum point, not z12.
>>> I have a curve of surface that is guaranteed to have one minimum.
>>> How would I use apache commons to find it?
>
> The current subversion tree provides an
> org.apache.commons.math.optimization package which contains a
> LevenbergMarquardt least squares solver. For a 2D surface in a 3D
> space, you could say your problem is to find the pair (x,y) that
> minimizes z^2 with z=f(x,y). For a 1D problem, you may prefer to solve
> f'(x) = 0 using one of the existing root solvers.
>
> The optimization code has not been released for now (it will be part of
> the 1.2 release), but it is quite stable. You will find examples in the
> archive of this list.
>
> Luc
>
>
> 
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