Dear all,
I’m having some problems getting optim with method="Nelder-Mead" to work
properly. It seems like there is no way of controlling the step size,
and the step size seems to depend on the *difference* between the
initial values, which makes no sense. Example:
f=function(xy, mu1, mu2) {
print(xy)
dnorm(xy[1]-mu1)*dnorm(xy[2]-mu2)
}
f1=function(xy) -f(xy, 0, 0)
optim(c(1,1), f1)
The first four values evaluated are
1.0, 1.0
1.1, 1.0
1.0, 1.1
0.9, 1.1
which is reasonable (step size of 0.1) for this function. And if I
translate both the function and the initial values
f2=function(xy) -f(xy, 5000, 5000)
optim(c(5001,5001), f2)
the first four values are
5001.0, 5001.0
5501.1, 5001.0
5001.0, 5501.1
4500.9, 5501.1
With
f3=function(xy) -f(xy, 0, 5000)
optim(c(1,5001), f3)
they are
1.0, 5001.0
501.1, 5001.0
1.0, 5501.1
-499.1, 5501.1
and with
f4=function(xy) -f(xy, -3000, 50000)
optim(c(-2999,50001), f4)
-2999.0, 50001.0
2001.1, 50001.0
-2999.0, 55001.1
-7999.1, 55001.1
However, the function to optimise is the same in all cases, only
translated, not scaled, so the step size *should* be the same. From
reading the documentation, it looks like changing the parscale should
work, and *relative* changes have the intended effect. Example:
optim(c(1,1), f1, control=list(parscale=c(1,5)))
gives the function evaluations
1.0, 1.0
1.1, 1.0
1.0, 1.5
1.1, 0.5
But changing both values, e.g.,
optim(c(1,1), f1, control=list(parscale=c(500,500)))
gives the same first four values. There *are* eventually some
differences in the values tried, but these don’t seem to correspond to
parscale as described in ?optim. For example, for parscale=c(1,1), the
parameter values tried are
1: 1, 1
2: 1.1, 1
3: 1, 1.1
4: 0.9, 1.1
5: 0.95, 1.075
6: 0.9, 1
7: 0.85, 0.95
8: 0.95, 0.85
9: 0.9375, 0.9125
10: 0.8, 0.8
11: 0.7, 0.7
12: 0.8, 0.6
13: 0.8125, 0.6875
14: 0.55, 0.45
while for parscale=c(500,500) they are
1: 1, 1
2: 1.1, 1
3: 1, 1.1
4: 0.9, 1.1
5: 0.95, 1.075
6: 0.9, 1
7: 0.85, 0.95
8: 0.95, 0.85
9: 0.975, 0.725
10: 0.825, 0.675
11: 0.7375, 0.5125
12: 0.8625, 0.2875
13: 0.859375, 0.453125
14: 0.625000000000001, 0.0750000000000004
for parscale=1/c(50000,50000) they are
1: 1, 1
2: 1.1, 1
3: 1, 1.1
4: 0.9, 1.1
5: 0.95, 1.075
6: 0.9, 1
7: 0.85, 0.95
8: 0.95, 0.85
9: 0.9375, 0.9125
10: 0.8, 0.8
11: 0.7, 0.7
12: 0.8, 0.6
13: 0.8125, 0.6875
14: 0.55, 0.45
And there seems to be no way of actually changing the step size to
reasonable values (i.e., the same values for optimising f1–f4).
Is there something I have missed in how one is supposed to use optim
with Nelder-Mead? Or is this actually a bug in the implementation?
$ sessionInfo()
R version 2.15.1 (2012-06-22)
Platform: x86_64-suse-linux-gnu (64-bit)
locale:
[1] LC_CTYPE=nn_NO.UTF-8 LC_NUMERIC=C
[3] LC_TIME=nn_NO.UTF-8 LC_COLLATE=nn_NO.UTF-8
[5] LC_MONETARY=nn_NO.UTF-8 LC_MESSAGES=nn_NO.UTF-8
[7] LC_PAPER=C LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=nn_NO.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
--
Karl Ove Hufthammer
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