[R] Constrained optimization

[Martin Maechler]

>>>>> "FCharles" == Charles Annis, P E <Charles.Annis at statisticalengineering.com>
>>>>>     on Mon, 16 Jun 2003 13:19:50 -0400 writes:

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

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

    FCharles> I would be grateful for any algorithmic
    FCharles> suggestions.

I'm astonished that your perusing of the archives and the
on-line help system didn't find 
	optim().

It has many methods, one of which working with box constraints.
I'm urging you to read help(optim) {and please read to the end
even if it's long}.

If you have non-box constraints, there are other tricks
(eg. continuous border penalizing) but it really depends on 
your application.

Martin Maechler <maechler at stat.math.ethz.ch>	http://stat.ethz.ch/~maechler/
Seminar fuer Statistik, ETH-Zentrum  LEO C16	Leonhardstr. 27
ETH (Federal Inst. Technology)	8092 Zurich	SWITZERLAND
phone: x-41-1-632-3408		fax: ...-1228			<><