R devel - Apr 2005 - "wild" function example in optim

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?
 
Many thanks in advance to all of you and kind regards,
Tom

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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

 	-thomas


 	-thomas

I have no words. Thank you so much for all your answers. This was just great. 
Thanks again and regards,
Tom


Peter Dalgaard <p.dalgaard@biostat.ku.dk> wrote:
Thomas Lumley writes:
> 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
It also depends on the optimizer. The SANN optimizer basically jumps
haphazardly (well, a bit more intelligently than that) back and forth
along the x axis and then "cools down" in order to settle in the
"best" local minimum. The parscale plays a role in setting the scale
of those jumps and if it is too low it might not wander far enough to
get near the true minimum.

For further information, you really need to do your own reading.
References are given on the help page.

-- 
O__ ---- Peter Dalgaard Blegdamsvej 3 
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N 
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk) FAX: (+45) 35327907

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