[R] Constrained non-linear optimisation

[David Beacham]

I'm relatively new to R, but I'm attempting to do a non-linear maximum 
likelihood estimation (mle) in R, with the added problem that I have a 
non-linear constraint.

The basic problem is linear in the parameters (a_i) and has only one 
non-linear component, b, with the problem being linear when b = 0 and 
non-linear otherwise. Furthermore, f(a_i) <= b <= g(a_i) for some 
(simple) f and g.

Using optim, I can get the optimisation to work when the non-linearity 
is included but not constrained, but gives poor results (as I'd expect). 
However, I'm not sure how best to go about the constraint condition. My 
initial attempts revolve around the use of logarithmic barrier function, 
but this only appears to work when using method="CG". When using "BFGS", 
the value of b 'goes out of bounds' and the loglikelihood starts 
throwing NaN, which is particularly bad if I want to box constrain the 
a_i using the "L-BFGS-B" method.

Are there any other methods/approaches/variations on the above available 
to me in the form of other packages/R functions etc? Or any good 
references/books to help me out?

Any help would be greatly appreciated,
David.