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 <[EMAIL PROTECTED]> 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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