Solving x'Ax==1 under constraints

Hi,

the matrix A is 5x5. I would like to find a solution to:

x'Ax==1, where x'=(x1,x2,x3,x4,x5) and x=(x1,x2,x3,x4,x5)'.

I have the following constraints:

x1+x2+x3+x4+x5=1

0<x(i)<0.25

I would like to find x1, x2, x3, x4 and x5.

Thank you very much.

[Jan]

What have you tried so far?

[Jhon Dukester]

I am kind of stock there. I have: lb= repmat(0,size(x)) ub=repmat(0.25,size(x))

Than, I don't know what to do.

[Roger Stafford]

You have five variables to solve for but only two equations. In spite of your inequality constraints there will in general be a three-dimensional infinite continuum of solutions. You need three more equations to reduce this system to one possessing a only a finite set of solutions.

As it stands it is not a well-formulated problem unless you merely wish to describe the boundaries of such a three-dimensional infinitude. It is analogous to a problem where one linear equation is given in three variables which restricts you to a certain two-dimensional plane and then giving three inequalities which confine you to the interior of a triangle in that plane. You would be asking for the "solution" when the infinitely many points within the triangle all satisfy your conditions.

[Jhon Dukester]

Ok, thank you!