Re: [Rd] "wild" function example in optim

[Prof Brian Ripley]

On Tue, 26 Apr 2005, Thomas Lumley wrote:
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.
Note that there the method is "SANN".  That makes assumptions about step 
sizes, in fact using a spherical Gaussian distribution of fixed size.  So 
parscale=20 is telling it to make initial steps large enough to explore 
the `blobs'. In particular, parscale is not set for the BFGS call in that 
example.

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)
Not necessarily.  The finite-differencing is done in units rescaled by 
parscale.  So a unit change in a single parameter needs to be a 
reasonably-sized step.  One can always set fnscale and neps, but it is 
easier to set parscale.

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))$par
[1] 1.673141e-15
but without g
optim(7,f,method="CG",control=list(parscale=1e5))$par
[1] 1.209735e-14
optim(7,f,method="CG",control=list(fnscale=1e-10))$par
[1] 1.997947e-11
--
Brian D. Ripley,                  [EMAIL PROTECTED]
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595
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