This looks really neat, but not being a mathematical programming consultant, I am a bit mystified by references to MINLP and BARON. I assume that the former is an algorithm and the latter is mathematical software. Can it be reimplemented in R?
Sorry about that (I use these terms daily and too often assume they are well-known in the "normal" world):
MINLP is Mixed Integer Nonlinear Programming, i.e. a constrained nonlinear optimization problem where some of the variables can assume only discrete values.
Here is an overview: http://coral.ie.lehigh.edu/presentations/siopt-05-minlp-handout.pdf
Baron is actually a very complex algorithm. I doubt it is easy to re-implement this in R, but an R interface may be doable. Here is some information: http://archimedes.cheme.cmu.edu/baron/baron.html