[R] Problem with constrained optimization with maxBFGS

[Prof. John C Nash]

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.
> 
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