Solving x'Ax==1 under constraints

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Jhon Dukester 2014-4-1

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评论： Jhon Dukester 2014-4-4

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.

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Roger Stafford 2014-4-2

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 2014-4-4