[R] Constrained optimization

[Charles Annis, P.E.]

Greetings, R-Wizards:

Earlier this week I requested help with trying to find an extremum subject
to a nonlinear constraint.  Many thanks to Martin Maechler, Spencer Graves,
and Jonathan Baron, who all suggested optim() rather than nlm(), and to
Robert Gentleman who suggested using a half-interval search, and special
thanks to Patrick Burns and David Khabie-Zeitoune who suggested ways to
create an appropriate objective function to use with optim().  

While working on the solution I took a closer look at the likelihood
profiles and reparameterized to avoid precipitous behavior in the
neighborhood of zero.  

Thus the solution for me was three-fold:

1) Re-parameterize to provide a less-asymmetric likelihood surface.

2) Use box constraints on the parameters to keep the solution-finding under
control and thus prevent excursions beyond the domain of parameter
feasibility.

3) Define an objective function that had the right objective!  ~:-)

Thanks to all for your help.

Charles Annis, P.E.

Charles.Annis at StatisticalEngineering.com
phone: 561-352-9699
eFAX: 503-217-5849
http://www.StatisticalEngineering.com