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.
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