optimization with inequalities
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