<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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