Infinite loop in `WolfLSZoom` when using stan for optimization

Summary:

Infinite loop in WolfLSZoom when using stan for optimization

Description:

When using Stan for optimization (with optimizing in rStan), the function WolfLSZoom (file bgfs_linesearch.hpp) is called, and causes infinite loop in some conditions.

When I run my script, it appears to be stuck in an infinite loop. Using Gdb on the code, I get the following values for local variables in the main loop of the WolfLSZoom function:

itNum = 59171617
alo = 0.73678486652303887
ahi = 0.73678486652303898

This indicates that there is indeed an infinite loop (itNum is high). The reason for that is that the loop is expected to terminate when ahi-alo < min_range, but ahi and alo stay constant because of rounding errors in the loop, and, in my particular case, ahi-alo = 2^(-53) > min_range = 10^(-16).

Do we expect to always have abs(ahi) < 1 and abs(alo) < 1? If so, then a simple fix could be to choose a larger value for min_range (10^(-15) would do the trick).

Reproducible Steps:

The bug is 100% reproducible with my R script, but, unfortunately, I cannot publish the source code of my example.

Version:

I am using rStan 2.21.8, but the bug seems to still exist in Stan's sources.

Start in bgfs_linesearch.hpp at the WolfLSZoom main loop and inspect how alo, ahi, itNum, and min_range interact when rounding prevents the interval from changing. Reproduce the reported boundary case if possible, then define a regression test that confirms the loop terminates without changing unrelated optimization behavior.