[R] optimization with inequalities

[Peter Dalgaard]

Florent Bresson <f_bresson at yahoo.fr> writes:

> 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 ?

If you think the boundaries in lower=c(....) are recomputed as the
iteration progresses, you're wrong. L-BGFS-B does box constraints
only. Instead parametrize using

q1=p1+p3
q2=p1+p2+p3
q3=p3

which is easily inverted to get the p's from the q's. Then optimize as
a function of q1..q3, substituting the inversion in the expression for
func (which btw needs to be a _function_), using the relevant box
constraints. 

-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907