[R] optim bug/help?

[rkevinburton at charter.net]

I was just trying to get a feel for the general strengths and weaknesses of the algoritmns. This is obviously a "demo" function and probably not representative of the "real" optimization problems that I will face. My concern was that if there is inaccuracy when I know the answer it might be worse when I don't if I don't understand the characteristics of the algoritmns involved.

Kevin

---- Ben Bolker <bolker at ufl.edu> wrote: 
>  <rkevinburton <at> charter.net> writes:
> 
> > 
> > In the documentation for 'optim' it gives the following function:
> > 
> > fr <- function(x) {   ## Rosenbrock Banana function
> >     x1 <- x[1]
> >     x2 <- x[2]
> >     100 * (x2 - x1 * x1)^2 + (1 - x1)^2
> > }
> > optim(c(-1.2,1), fr)
> > 
> > When I run this code I get:
> > 
> > $par
> > [1] 1.000260 1.000506
> > 
> > I am sure I am missing something but why isn't 1,1 a better answer? If I plug
> 1,1 in the function it seems that
> > the function is zero. Whereas the answer given gives a function result of
> 8.82e-8. This was after 195 calls
> > to the function (as reported by optim). The documentation indicates that the
> 'reltol' is about 1e-8. Is
> > this the limit that I am bumping up against?
> > 
> > Kevin
> > 
> 
>   Yes, this is basically just numeric fuzz, the
> bulk of which probably comes from finite-difference
> evaluation of the derivative.
> As demonstrated below, you can get a lot closer
> by defining an analytic gradient function.
> May I ask why this level of accuracy is important?
> (Insert Tukey quotation here about approximate answers
> to the right question here ...)
> 
>   Ben Bolker
> ---------
> 
> fr <- function(x) {   ## Rosenbrock Banana function
>     x1 <- x[1]
>     x2 <- x[2]
>     100 * (x2 - x1 * x1)^2 + (1 - x1)^2
> }
> 
> ## gradient function
> frg <- function(x) {
>   x1 <- x[1]
>   x2 <- x[2]
>   c(100*(4*x1^3-2*x2*2*x1)-2+2*x1,
>     100*(2*x2-2*x1^2))
> }
> 
> ## use numericDeriv to double-check my calculus
> x1 <- 1.5
> x2 <- 1.7
> numericDeriv(quote(fr(c(x1,x2))),c("x1","x2"))
> frg(c(x1,x2))
> 
> ##
> optim(c(-1.2,1), fr)  ## Nelder-Mead
> optim(c(-1.2,1), fr,method="BFGS")
> optim(c(-1.2,1), fr, gr=frg,method="BFGS")  ## use gradient
> 
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