Re: nlminb with constraints

["Douglas Bates" <bates@stat.wisc.edu>]

On 8/22/07, John Pitchard <johnpitchard@googlemail.com> wrote:
> Dear all,

> I have a function that I want to minimise, it is in the form of a vector.
> However, there is a restriction on the actual vector itself, e.g. if the
> vector,x, has n components then

> x[n] <- 1 -(x[1] + ...+x[n-1]).

> Does anyone know how to put this constraint into the nlminb function?

With an equality constraint like this you define the objective as a
function of x[1], ..., x[n-1] and internally evaluate x[n] from the
other values.

Do the x's represent probabilities by any chance?  If so, the
constraints are more complicated because you must have x[i] >= 0, i =
1,...,n.  One way of enforcing this is to use a multivariate version
of a logistic transformation.  David Jupp used a version of this in a
paper on free-knot splines.  Don Watts and I describe such a
transformation in our 1988 Wiley book "Nonlinear Regression Analysis
and Its Applications".