Linear least squares with constraints

Hi,

I'm not completely familiar with these sorts of problems, so please bear with me.

Given a homogeneous system

where is a x symmetric matrix:

From what I understand, the eigenvectors of are the set of best fitting solutions to the system above, however, I require a solution that is positive and constrained to a range.

Assuming that you have a vector of eigenvalues in descending order, and the eigenvectors corresponding to them as the columns of a matrix , select an index such that

subject to

where is a vector with all elements equal to 1

and

The way I'm interpreting the minimisation above is: minimise the square of the Euclidean norm of subject to all the elements of the solution being in the range . What's the significance of the subscript here? I don't believe it's constrained in any way.

How can I solve this?

Thanks.

P.S. In case anyone is wondering, these equations are from "NURBS curve and surface fitting for reverse engineering, W. Ma and J. -P. Kruth"