[R-sig-ME] Comparing optimizers for lmer

[Douglas Bates]

Colin Longhurst and I have been comparing optimizers with lmer on several
examples of linear mixed-effects models.  We included gradient-based and
derivative-free optimizers using lmm from the MixedModels package for Julia
in our comparisons.

The results are available as a github repository in the form or an R
package. It is installed by first installing the devtools package then
running

devtools::install_github("Stat990-033/Timings")

A summary of the results in the form of an IPython (or IJulia, in this
case) notebook can be accessed as

https://github.com/Stat990-033/Timings/blob/master/inst/doc/Summaries.ipynb

This should display as a notebook in your browser.  If you clone the
repository and have Julia installed along with the packages required, you
can rerun the results on your computer to see what timings it gives.

The bottom line is that the most reliable of the optimizers we tried in R
are NLOPT_LN_BOBYQA from the nloptr package and L-BFGS-B and nlminb from
the optimx package.  Of these NLOPT_LN_BOBYQA is generally the fastest and
I have recommended to my co-authors of the lme4 package that it become the
default.

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