[R] nlm question

[Peter Dalgaard]

Thomas Lumley <tlumley at u.washington.edu> writes:

> You might want to look at the function surface, eg:
> 
>    dd<-expand.grid(x=seq(0,2,length=20),y=seq(0,2,length=20))
>    yy<-apply(dd,1,mfun1)
>    contour(seq(0,2,length=20),seq(0,2,length=20),matrix(yy,20),nlevels=40)
> 
> The function is nearly flat on a fairly wide band where either x or y
> is 1 or slightly larger, and so is far from quadratic in that region.
> You need better starting values, or some rescaling of the objective
> function.

A slight modification is quite revealing:

 dd<-expand.grid(x=seq(-1,2,length=100),y=seq(-1,2,length=100))
 yy<-apply(dd,1,mfun1)
 persp(seq(-1,2,length=100),seq(-1,2,length=100),matrix(yy,100)^.1)

 contour(seq(-1,2,length=100),seq(-1,2,length=100),matrix(yy,100)^.1)
 abline(v=1.485,h=0)

> Another optimisation algorithm might give different results, and in
> fact if you try optim() you end up at (1,1) with method="Nelder-Mead"
> and method="BFGS", but at (1.48,0) with "CG" or "L-BFGS-B".

And SANN found (1,1) two times out of three for me, the third one
getting stuck in the 3rd local minimum at (-0.72,1.22)
-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907