"wild" function example in optim

On Tue, 26 Apr 2005, Werner Bier wrote:

Dear all,

Firstly, I do apologize if my question is simple and posted in the
wrong place but I had no reply from the R-help mailing list (maybe
it is too simple!).

I was wondering why parscale is set to 20 in the "wild" function
example used in ?optim. This function has only one parameter and if
we set parscale equal to 1 then the solution near the global minimum
is not found.

I would use parscale only in cases the object function has more than
one parameter to be optimised, shouldn't I?

parscale is more important in cases with more than one parameter (and
with one parameter you could set fnscale instead of parscale to get
the same effect)

However, a sufficiently badly scaled one-d problem can still benefit
from fnscale or parscale.

f

function(x) 1e-10*x^2

g

function(x) 2e-10*x

optim(7,f,g,method="CG")$par

[1] 7

optim(7,f,g,method="CG",control=list(parscale=1e5))$par

[1] 1.209735e-14

optim(7,f,g,method="CG",control=list(fnscale=1e-10))$par

[1] 1.673141e-15