Hi, thank you very much for the reply!
Consider minimize quadratic form w'Aw with A be the following matrix.
> Dmat/2
[,1] [,2] [,3]
[1,] 1.0 0.5 0.8
[2,] 0.5 1.0 0.9
[3,] 0.8 0.9 1.0
I need to find w=(w1,w2,w3), a 3 by 1 vector, such that sum(w)=3, and wi>=0
for all i.
Below is the code I wrote, using the function solve.QP , however, the
solution for w still have a
negtive component. Can some one give me some suggestions?
Thank you very much!
> x <- 2*c(1,0.5,0.8,0.5,1,0.9, 0.8,0.9,1)
> Dmat <- matrix(x, byrow=T, nrow=3, ncol=3)
> dvec <- numeric(3)
> Amat <- matrix(0,3,4)
> Amat[,1 ] <- c(1,1,1)
> Amat[,2:4 ]<- t(diag(3))
> bvec <- c(3,0,0,0)
>
> solve.QP(Dmat,dvec,Amat,bvec=bvec)
$solution
[1] 1.500000e+00 1.500000e+00 -8.881784e-16
$value
[1] 6.75
$unconstrained.solution
[1] 0 0 0
$iterations
[1] 3 0
$Lagrangian
[1] 4.5 0.0 0.0 0.6
$iact
[1] 1 4
2010/4/10 Gabor Grothendieck <[email protected]>
> Check out the quadprog package.
>
> On Sat, Apr 10, 2010 at 5:36 PM, li li <[email protected]> wrote:
> > Hi, thanks for the reply.
> > A will be a given matrix satisfying condition 1. I want to find the
> > vector w that minimizes the
> > quadratic form. w satisfies condition 2.
> >
> >
> > 2010/4/10 Paul Smith <[email protected]>
> >
> >> On Sat, Apr 10, 2010 at 5:13 PM, Paul Smith <[email protected]> wrote:
> >> >> I am trying to minimize the quardratic form w'Aw, with certain
> >> >> constraints.
> >> >> In particular,
> >> >> (1) A=(a_{ij}) is n by n matrix and it is symmetric positive
> >> definite,
> >> >> a_{ii}=1 for all i;
> >> >> and 0<a_{ij}<1 for i not equal j.
> >> >> (2) w'1=n;
> >> >> (3) w_{i}>=0
> >> >>
> >> >> Analytically, for n=2, it is easy to come up with a result. For
> larger
> >> n, it
> >> >> seems
> >> >> difficult to obtain the result.
> >> >>
> >> >> Does any one know whether it is possible to use R to numerically
> compute
> >> it?
> >> >
> >> > And your decision variables are? Both w[i] and a[i,j] ?
> >>
> >> In addition, what do you mean by "larger n"? n = 20 is already large
> >> (in your sense)?
> >>
> >> Paul
> >>
> >> ______________________________________________
> >> [email protected] mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide
> >> http://www.R-project.org/posting-guide.html<http://www.r-project.org/posting-guide.html>
> <http://www.r-project.org/posting-guide.html>
> >> and provide commented, minimal, self-contained, reproducible code.
> >>
> >
> > [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > [email protected] mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html<http://www.r-project.org/posting-guide.html>
> > and provide commented, minimal, self-contained, reproducible code.
> >
>
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