[R] Constrained optimization

[Charles Annis, P.E.]

Greetings, R-Wizards: 

I'm trying to find an extremum subject to a nonlinear constraint.  (Yes, I
have perused the archives but have found nothing positive.) The details of
the problem are these:

In a paper published some years ago in Technometrics, ("Confidence bands for
cumulative distribution functions of continuous random variables"
Technometrics, 25, 77-86. 1983), Cheng and Iles describe an ingenious method
for placing confidence bounds on an entire cdf by defining the likelihood
ratio confidence "ellipse" for the model parameters, and then traversing the
periphery and finding the most extreme values for x, at a given F(x), such
that the distribution parameters reside on that confidence contour.  (Well,
their method is more sophisticated than that, but that's essentially how it
works.)  I implemented the thing in a spreadsheet 15 years ago, and would
like to do the same in R.  But EXCEL's solver can find an extremum subject
to a constraint, and I haven't figured out how to get nlm() to do that.

I would be grateful for any algorithmic suggestions.

Many Thanks.

Charles Annis, P.E.

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