1. A method for using a computer system to solve a global optimization problem specified by a function ƒ and a set of equality constraints, the method comprising: receiving a representation of the function ƒ and the set of equality constraints q i(x)&equals; 0(i&equals;1,..., r) at the computer system, wherein ƒ is a scalar function of a vector x&equals;(x 1, x 2, x 3,... X n ); storing the representation in a memory within the computer system; performing an interval equality constrained global optimization process to compute guaranteed bounds on a globally minimum value of the function ƒ(x) subject to the set of equality constraints; wherein performing the interval equality constrained global optimization process involves, applying term consistency to a set of relations associated with the interval equality constrained global optimization problem over a 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 interval equality constrained global optimization problem over the subbox X, and excluding any portion of the subbox X that violates any of the relations, and performing an interval Newton step for the interval equality constrained global optimization problem over the subbox X.