# [R] minimization function

Gabor Grothendieck ggrothendieck at gmail.com
Sun Apr 11 18:54:25 CEST 2010

```It works for me:

> 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, meq=1)
\$solution
[1] 1.5 1.5 0.0

\$value
[1] 6.75

\$unconstrained.solution
[1] 0 0 0

\$iterations
[1] 3 0

\$iact
[1] 1 4

>
> R.version.string
[1] "R version 2.10.1 (2009-12-14)"
> win.version()
[1] "Windows Vista (build 6002) Service Pack 2"
[1] "1.4-12"

On Sun, Apr 11, 2010 at 11:31 AM, li li <hannah.hlx at gmail.com> wrote:
> Hi,
>  thanks!
>
> I added meq=1 and it did not seem to work. The result is the same as before.
>
>> 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, meq=1)
> \$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
>>
>
>
> 2010/4/11 Gabor Grothendieck <ggrothendieck at gmail.com>
>>
>> Add meq=1 to the arguments.
>>
>> On Sun, Apr 11, 2010 at 9:50 AM, li li <hannah.hlx at gmail.com> wrote:
>> > 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 <ggrothendieck at gmail.com>
>> >>
>> >> Check out the quadprog package.
>> >>
>> >> On Sat, Apr 10, 2010 at 5:36 PM, li li <hannah.hlx at gmail.com> 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 <phhs80 at gmail.com>
>> >> >
>> >> >> On Sat, Apr 10, 2010 at 5:13 PM, Paul Smith <phhs80 at gmail.com>
>> >> >> 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
>> >> >>
>> >> >> ______________________________________________
>> >> >> R-help at r-project.org mailing list
>> >> >> https://stat.ethz.ch/mailman/listinfo/r-help
>> >> >>
>> >> >>
>> >> >> 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]]
>> >> >
>> >> > ______________________________________________
>> >> > R-help at r-project.org mailing list
>> >> > https://stat.ethz.ch/mailman/listinfo/r-help