R help - May 2011 - Problem with constrained optimization with maxBFGS

Dear all,

I need to maximize the v:

 v= D' W D


D is a column vector ( n , 1)
W is a given matrix (n, n)

subject to:
 sum D= 1

(BTW, n is less than 300)
I´ve tried to use maxBFGS, as follows:

#####################################
objectiveFunction<-function(x)
{
  return(t(D)%*%W%*%D)
}

Amat<-diag(nrow(D))
Amat<-rbind((rep(-1, nrow(D))), Amat)
bvec<-matrix( c(0), nrow(D)+1, 1)
bvec[1,1]<-c(1)
startValues=rep(1/nrow(D),nrow(D)) #Istart value is homogeneous distribution
res <<- maxBFGS(objectiveFunction, start=startValues,
constraints=list(ineqA=Amat, ineqB=bvec))
########################################
The outcome is equal to the startValues. I´ve tried several initial values
and nothing changes.
Please, what am I doing wrong? Any suggestion?

Thanks a lot!

Leo.

	[[alternative HTML version deleted]]

Is this a homework problem in finding the largest eigensolution of W?

If not, I'd be trying to maximize (D' W D)/ (D' D)

using (n-1) values of D and setting one value to 1 -- hopefully a value that is
not going
to be zero.

JN

> 
> Date: Wed, 11 May 2011 17:28:54 -0300
> From: Leonardo Monasterio <leonardo.monasterio at gmail.com>
> To: r-help at r-project.org
> Subject: [R] Problem with constrained optimization with maxBFGS
> Message-ID: <BANLkTimJ0quyHgPA2ycMzO4ZPkhgPomNbw at mail.gmail.com>
> Content-Type: text/plain
> 
> Dear all,
> 
> I need to maximize the v:
> 
>  v= D' W D
> 
> 
> D is a column vector ( n , 1)
> W is a given matrix (n, n)
> 
> subject to:
>  sum D= 1
> 
> (BTW, n is less than 300)
> I?ve tried to use maxBFGS, as follows:
> 
> #####################################
> objectiveFunction<-function(x)
> {
>   return(t(D)%*%W%*%D)
> }
> 
> Amat<-diag(nrow(D))
> Amat<-rbind((rep(-1, nrow(D))), Amat)
> bvec<-matrix( c(0), nrow(D)+1, 1)
> bvec[1,1]<-c(1)
> startValues=rep(1/nrow(D),nrow(D)) #Istart value is homogeneous
distribution
> res <<- maxBFGS(objectiveFunction, start=startValues,
> constraints=list(ineqA=Amat, ineqB=bvec))
> ########################################
> The outcome is equal to the startValues. I?ve tried several initial values
> and nothing changes.
> Please, what am I doing wrong? Any suggestion?
> 
> Thanks a lot!
> 
> Leo.
> 
> 	[[alternative HTML version deleted]]
> 
> 
> 
> -