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@gmail.com>

> On Sat, Apr 10, 2010 at 5:13 PM, Paul Smith <phhs80@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
>
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