automatically try different initial values in optim - r

Question

I use optim(.) to try to find the best fitting parameters for some function fn(dat, par, out=FALSE) where par must be a vector of two elements and out determines the output format. I use
optim(par=c(1,1), fn, dat=dat)
to identify the best-fitting values of par. Depending on the data in dat, this either works ot throws an error that
function cannot be evaluated at initial parameters
which I understand requires different starting values for optim(.). My problem is that I apply the function to many data sets in parallel and wonder whether I indeed need to try different values by hand or whether there is some way of automatizing this along the lines of
if no error then great
if error try par=c(0.5,1)
if no error then great
if error try par=c(0.5,0.5)
...

Answer 1

You could run a grid search before you start and discard NA parameters. Here is an example.
A test function:
fn <- function(x) {
if (x[1] < 0)
NA
else
prod(x)
}
Now run a grid search.
library("NMOF")
res <- gridSearch(fn,
npar = 2, ## length of x
lower = -1, ## lower bound for x
upper = 3, ## upper bound for x
n = 5) ## number of levels per element in x
## 2 variables with 5, 5 levels: 25 function evaluations required.
The function shows you all the parameter combinations it tried.
res$levels
## [[1]]
## [1] -1 -1
##
## [[2]]
## [1] 0 -1
##
## [[3]]
## [1] 1 -1
##
## ....
And it provides the objective function values associated with these combinations.
res$values
## [1] NA 0 -1 -2 -3 NA 0 0 0 0 NA 0 1 2 3
## [16] NA 0 2 4 6 NA 0 3 6 9
## => many objective functions values are NA
The best (none-NA) solution:
res$minlevels
## [1] 3 -1
## => your starting value for optim:
##
## optim(gridSearch(fn, npar = 2,
## lower = -1, upper = 3, n = 5)$minlevels,
## fn, dat = dat)
Of course, this won't give you a guarantee that at least one none-NAvector is found, but the chances may improve.