[R] optimization with inequalities

Prof Brian Ripley ripley at stats.ox.ac.uk
Mon Nov 28 17:12:31 CET 2005

```On Mon, 28 Nov 2005, Florent Bresson wrote:

> I have to estimate the following model for several
> group of observations :
>
> y(1-y) = p[1]*(x^2-y) + p[2]*y*(x-1) + p[3]*(x-y)
>
> with constraints :
> p[1]+p[3] >= 1
> p[1]+p[2]+p[3]+1 >= 0
> p[3] >= 0
>
> I use the following code :
> func <- sum((y(1-y) - p[1]*(x^2-y) + p[2]*y*(x-1) +
> p[3]*(x-y))^2)
> estim <- optim( c(1,0,0),func, method="L-BFGS-B" ,
> lower=c(1-p[3], -p[1]-p[3]-1, 0) )
>
> and for some group of observations, I observe that the
> estimated parameters don't respect the constraints,
> espacially the first. Where's the problem please ?

User mis-reading the help page!

L-BFGS-B handles `box constraints', not linear inequality constraints.
You can reparametrize to make these box constraints: use p[3], p[1]+p[3]
and p[1]+p[2]+p[3] are variables.

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

```