[EMAIL PROTECTED] a écrit :
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.
You are right, but currently we provide least squares only. If you know
a low bounding value (say -100 or -1.Oe6), you can use (z + low)^2. The
limitation to least-squares problems comes from the Levenberg-Marquardt
algorithm. For a more general minimizer (not for quadratic forms), you
may try to modify the Gauss-Newton algorithm implementation. The
classical algorithm is not specialized, but my current implementation in
[math] is. I dealt with least squares problems only when I wrote this.
We should certainly refactor this and provide a general minimizing
package with a classical GN, steepest descent and also conjugate
gradient. We could use them as a basis for some least-squares solvers
(and also keep the very efficient and specialized Levenberg-Marquardt
too). Such a new package would be nice for 2.0. For now we are trying to
finalize 1.2. You can open a JIRA ticket to make sure we do not forget
this need.
Luc
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
Levenberg-Marquardt 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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