[R] Problem with constrained optimization with maxBFGS

[peter dalgaard]

On May 13, 2011, at 00:15 , Prof. John C Nash wrote:

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

Not as stated. It said "sum D = 1", not "sum D^2 =1". With a linear constraint, it looks like weighted least squares, but then you should be minimizing, not maximizing. As stated, I'd say that the objective is unbounded, so something is amiss...

> 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]]
>> 
>> 
>> 
>> -
> 
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-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com