Some interesting notes:
From: http://user2014.stat.ucla.edu/files/tutorial_Nash_slides.pdf:
My opinion: I think GAMS and R non-linear optimization really targets different audiences and different model types (R: smaller models with emphasis on parameter estimation and zero or few constraints; GAMS: large, sparse and more complex models with many constraints). Matlab and R may be seen a little bit more as direct “competitors” with respect to the type models they typically solve.
Amazon seems to confirm people are using R to do optimization:
