Constrained fits: y~a+b*x-c*x^2, with a,b,c >=0

I wonder whether R has methods for constrained fitting of linear
models.

I am trying fm<-lm(y~x+I(x^2), data=dat) which most of the time gives
indeed the coefficients of an inverted parabola. I know in advance
that it has to be an inverted parabola with the maximum constrained to
positive (or zero) values of x.

The help pages for lm do not contain any info on constrained fitting.

Does anyone know how to?

G'day Alex,

On Wed, 27 May 2009 11:51:39 +0200
Alex van der Spek <amvds at xs4all.nl> wrote:

I wonder whether R has methods for constrained fitting of linear
models.

I am trying fm<-lm(y~x+I(x^2), data=dat) which most of the 

time gives

indeed the coefficients of an inverted parabola. I know in advance
that it has to be an inverted parabola with the maximum 

constrained to

positive (or zero) values of x.

The help pages for lm do not contain any info on 

constrained fitting.

Does anyone know how to?

Look at the package nnls on CRAN.

According to your subject line, you are trying to solve what is known
as a quadratic program, and there are at least two quadratic
programming solvers (ipop in kernlab and solve.qp in quadprog)
available for R.

HTH.

Cheers,

	Berwin

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