[Rd] Bug in optim for specific orders of magnitude

[Steven Dirkse]

Collin,

It is interesting that you get such strange results when passing denormal
values to optim().  Several possibilities for this spring to mind.

A better question though might be, "What kind of results are you expecting
when you pass such small values to optim()?"  In general, you shouldn't
have a strong expectation that you'll get good results back when you have
small coefficients like 1e-317 (or 1e-17) in your objective function.  The
algorithms behind optim() are not designed or implemented to do their best
work with coefficients of magnitude far from 1.  You can hope.  You can get
lucky.  But I would not advise you to have strong expectations.

-Steve

On Fri, Dec 23, 2022 at 1:20 PM Collin Erickson <collinberickson using gmail.com>
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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-- 
Steven Dirkse, Ph.D.
GAMS Development Corp.
office: 202.342.0180

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