From: Martin Maechler (maechler@stat.math.ethz.ch)
Date: Tue 17 Jun 2003 - 17:42:04 EST
Message-id: <16110.50764.604685.473921@gargle.gargle.HOWL>
>>>>> "FCharles" == Charles Annis, P E <Charles.Annis@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@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 <><
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