R help - Apr 2010 - minimization function

Hi all,
    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?

Thank you so much in advance!


Hannah

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On Sat, Apr 10, 2010 at 4:58 PM, li li <hannah.hlx 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] ?

Paul