[Rd] Bug in optim for specific orders of magnitude

[Duncan Murdoch]

The optim help page mentions scaling in the discussion of the "control" 
argument.  Specifically under the parscale description:

"Optimization is performed on par/parscale and these should be 
comparable in the sense that a unit change in any element produces about 
a unit change in the scaled value."

In your function a unit change in x[1] makes a change of 1e-317 in the 
function value, and changing x[2] has no effect at all.

It would be nice if violating the rule only led to inefficiencies or 
poor stopping decisions, but the numbers you are working with are close 
to the hardware limits (the smallest positive number with full precision 
is .Machine$double.xmin, about 2e-308), and sometimes that means 
assumptions in the code about how arithmetic works are violated, e.g. 
things like x*1.1 > x may not be true for positive x below 
.Machine$double.xmin .

Duncan Murdoch

On 23/12/2022 12:30 p.m., Collin Erickson wrote:
> 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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> 
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