1. A method for using a computer system to solve an unconstrained interval global optimization problem specified by a function f, wherein f is a scalar function of a vector x&equals;(x 1, x 2, x 3,... x n ), the method comprising: receiving a representation of the function f at the computer system; storing the representation in a memory within the computer system; and performing an interval global optimization process to compute guaranteed bounds on a globally minimum value of the function f(x) over a subbox X; wherein performing the interval global optimization process involves, applying term consistency to a set of relations associated with the function f over the subbox X, and excluding any portion of the subbox X that violates any of these relations, applying box consistency to the set of relations associated with the function f over the subbox X, and excluding any portion of the subbox X that violates any of these relations, and performing an interval Newton step on the subbox X to produce a resulting subbox Y, wherein the point of expansion of the interval Newton step is a point x within the subbox X, and wherein performing the interval Newton step involves evaluating the gradient g(x) of the function f(x) using interval arithmetic.