From p.dalgaard at biostat.ku.dk  Tue Apr 26 19:04:55 2005
From: p.dalgaard at biostat.ku.dk (Peter Dalgaard)
Date: Tue Apr 26 19:05:03 2005
Subject: [Rd] "wild" function example in optim
In-Reply-To: <Pine.A41.4.61b.0504260851450.131934@homer03.u.washington.edu>
References: <20050426154749.33905.qmail@web61201.mail.yahoo.com>
	<Pine.A41.4.61b.0504260851450.131934@homer03.u.washington.edu>
Message-ID: <x2ekcxsc3s.fsf@turmalin.kubism.ku.dk>

Thomas Lumley <tlumley@u.washington.edu> 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


[Rd] "wild" function example in optim
Peter Dalgaard