[Rd] optim(…?=, =?utf-8?Q?method=‘L-BFGS-B’) stops with an error message while violating the lower bound

[Avraham Adler]

I believe the code can be found here:
http://users.iems.northwestern.edu/~nocedal/lbfgsb.html. Specifically,
lbfgsb.f in version 3.0 starts:

This is a modified version of L-BFGS-B. Minor changes in the updated
c     code appear preceded by a line comment as follows
c
c     c-jlm-jn
c
c     Major changes are described in the accompanying paper:
c
c         Jorge Nocedal and Jose Luis Morales, Remark on "Algorithm 778:
c         L-BFGS-B: Fortran Subroutines for Large-Scale Bound Constrained
c         Optimization"  (2011). To appear in  ACM Transactions on
c         Mathematical Software,
c
c     The paper describes an improvement and a correction to Algorithm 778.
c     It is shown that the performance of the algorithm can be improved
c     significantly by making a relatively simple modication to the subspace
c     minimization phase. The correction concerns an error caused by the use
c     of routine dpmeps to estimate machine precision.


It is released under the New 3-clause BSD license, so porting it to C
for inclusion into R should be OK as long as the i's are dotted and
t's crossed.


Avi

On Mon, Oct 10, 2016 at 5:54 AM, Martin Maechler
<maechler at stat.math.ethz.ch> wrote:
>>>>>> Spencer Graves <spencer.graves at prodsyse.com>
>>>>>>     on Sat, 8 Oct 2016 18:03:43 -0500 writes:
>
> [.............]
>
>     >              2.  It would be interesting to know if the
>     > current algorithm behind optim and optimx with
>     > method='L-BFGS-B' incorporates Morales and Nocedal (2011)
>     > 'Remark on “Algorithm 778: L-BFGS-B: Fortran Subroutines
>     > for Large-Scale Bound Constrained Optimization”'.  I
>     > created this vignette and started this threat hoping that
>     > someone on the R Core team might decide it's worth
>     > checking things like that.
>
> well I hope you mean "thread" rather "threat"  ;-)
>
> I've now looked at the reference above, which is indeed quite
> interesting.
>         doi 10.1145/2049662.2049669
>         --> http://dl.acm.org/citation.cfm?doid=2049662.2049669
> A "free" (pre-publication I assume) version of the manuscript is
>   http://www.eecs.northwestern.edu/~morales/PSfiles/acm-remark.pdf
>
> The authors, Morales and Nocedal, the 2nd one being one of the
> original L-BFGS-B(1997) paper, make two remarks, the 2nd one
> about the "machine epsilon" used, and I can assure you that R's
> optim() version never suffered from that; we've always been
> using a C translation of the fortran code, and then used DBL_EPSILON.
> R's (main) source file for that is in .../src/appl/lbfgsb.c, e.g., here
> https://svn.r-project.org/R/trunk/src/appl/lbfgsb.c
>
> OTOH, their remark 1 is very relevant and promising faster /
> more reliable convergence.
> I'd be "happy" if optim() could gain a new option, say, "L-BFGS-B-2011"
> which would incorporate what they call "modified L-BFGS-B".
>
> However, I did not find published code to go together with their
> remark.
> Ideally, some of you interested in this, would provide a patch
> against the above  lbfgsb.c  file
>
> Martin Maechler,
> ETH Zurich
>
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