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NMinimize Method suboptions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg124153] NMinimize Method suboptions
*From*: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
*Date*: Wed, 11 Jan 2012 04:22:55 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
Dear all
I am fitting some experimental data using NonlinearModelFit. The model and
constraints can lead to some difficulty with convergence so I am using the
NMinimize method as follows:
fit = NonlinearModelFit[
data, {model, constr}, {pars}, var,
Weights -> 1/errors^2,
Method -> {NMinimize,
Method -> {"DifferentialEvolution",
"PostProcess" -> {FindMinimum, Method -> "QuasiNewton"}
}
}
]
(The Method suboption for the FindMinimum value of the "PostProcess"
option is undocumented, but the fact of its existence is obvious. In this
case, BFGS a.k.a. "QuasiNewton" is very effective for final refinement of
the differential evolution results.)
My questions are as follows:
1. We know that some possible values for the "PostProcess" option are
"KKT", "InteriorPoint", and FindMinimum (with the undocumented Method
suboption giving access to a rather wide range of possibilities). Are
there any others? And is there any difference between the option values
"InteriorPoint" and {FindMinimum, Method -> "InteriorPoint"}?
2. For the "DifferentialEvolution" method, the documentation states that
recombination is according to Storn and Price's rand/1 scheme. Are any
other schemes implemented? (In my opinion, there are not that many others
worth using, with the notable exceptions of best/2 and MDE5 [Thangaraj et
al., Appl. Math. Comp. 216 (2), 532 (2010)], which can significantly
outperform rand/1. This is particularly noticeable if the selection method
is also slightly modified so that rather than using a tournament approach,
the fitness values of all individuals are sorted and the best half of the
combined previous generation and mutant population is kept for the next
generation. However, this selection method does not work well with the
rand/1 scheme, which is probably why nobody else uses it as far as I know.)
Thanks for any answers,
Best,
O. R.
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