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In article <BtvrIE.IB8@research.canon.oz.au> enzo@research.canon.oz.au (Enzo Liguori) writes:
>I'd like suggestions on how to minimize a positive definite quadratic form with
>the variable constrained to be within an interval like:
>A<=Xi<=B
>with A,B constants and Xi any variable of the quadratic form.
>If there's a faster algorithm that works with simpler constraints like:
>Xi<=0
>Xj>=0
>Xk unconstrained
>that'll probably do.
>Thanks in advance.
>
>        Enzo
>
>Enzo Liguori - Canon Information Systems Research Australia

This problem is well known and has a systematic method for solving it.
The more general problem can also be solved (i.e., linear constraints
on the variable: a11x1+a12x2+...= b1 and so on).
You can refer to any non-linear programming book and look under "quadratic
programming". There is a book by K. G. Murty, "Linear complementarity, 
linear and nonlinear programming". Another book is "Nonlinear Programming
theory and algorithms" by Bazraa and Shetty.
By the way if the problem is uconstrained, write the system in the form
X^t.Q.X (t indicates transpose), then solve the system of equatios, 
Q.x = 0 ==> x=0 as a unique solution since Q is positive definite.
-Samer
.