[Rd] Bug in optim for specific orders of magnitude

[Collin Erickson]

Hello,

I've come across what seems to be a bug in optim that has become a nuisance
for me.

To recreate the bug, run:

optim(c(0,0), function(x) {x[1]*1e-317}, lower=c(-1,-1), upper=c(1,1),
method='L-BFGS-B')

The error message says:

Error in optim(c(0, 0), function(x) { :
  non-finite value supplied by optim

What makes this particularly treacherous is that this error only occurs for
specific powers. By running the following code you will find that the error
only occurs when the power is between -309 and -320; above and below that
work fine.

p <- 1:1000
giveserror <- rep(NA, length(p))
for (i in seq_along(p)) {
  tryout <- try({
    optim(c(0,0), function(x) {x[1]*10^-p[i]}, lower=c(-1,-1),
upper=c(1,1), method='L-BFGS-B')
  })
  giveserror[i] <- inherits(tryout, "try-error")
}
p[giveserror]

Obviously my function is much more complex than this and usually doesn't
fail, but this reprex demonstrates that this is a problem. To avoid the
error I may multiply by a factor or take the log, but it seems like a
legitimate bug that should be fixed.

I tried to look inside of optim to track down the error, but the error lies
within the external C code:

.External2(C_optim, par, fn1, gr1, method, con, lower,
        upper)

For reference, I am running R 4.2.2, but was also able to recreate this bug
on another device running R 4.1.2 and another running 4.0.3.

Thanks,
Collin Erickson

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