[R] Optimization of constrained linear least-squares problem

[Stefaan Lhermitte]

Dear R-ians,

I want to perform an linear unmixing of image pixels in fractions of 
pure endmembers. Therefore I need to perform a constrained linear 
least-squares problem that looks like :

min || Cx - d || ² where sum(x) = 1.

I have a 3x3 matrix C, containing the values for endmembers and I have a 
3x1 column vector d (for every pixel in the image). In theory my x 
values should all be in the (0,1) interval but I don't want to force 
them so I can check the validity of my solution. I just want to 
calculate the x values. Can anyone help me with this problem? I've been 
checking the optim, optimize, constrOptim and nlm help files, burt  I 
don't understand it very well. Wich function should I use for my 
problem? I did a first test using optim:

# Make my C matrix
EM<- c(4.5000,6.0000,10.5000,5.0000,27.0000,20.7500,16.7500,23.6666,38.7500)
C <- array(EM, c(3,3))

# Take an arbitrary d
d<-c(10, 20, 20)

# Define the function
 fr <- function(x) {
C[1,]*x=d
C[2,]*x=d
C[3,]*x=d
sum(x)=1}

# Perform the optimization
optim(c(0.25,0.25,0.25),fr)

But it did not work. I got the eror couldn't find function. Can anyone 
tell me what functyion I should use for my problem and how should I 
program it?

Thanx in advance,
Stef