One embodiment of the present invention provides a system that solves a global optimization problem specified by a function f and a set of equality constraints q.sub.1(x)=0 (i=1, . . . , r), wherein f is a scalar function of a vector x=(x.sub.1, x.sub.2, x.sub.3, . . . x.sub.n). During operation, the system receives a representation of the function f and the set of equality constraints and stores the representation in a memory within a computer system. Next, the system and performs an interval global optimization process to compute guaranteed bounds on a globally minimum value of the function f(x) subject to the set of equality constraints. Performing this interval global optimization process involves, applying term consistency to the set of equality constraints over a subbox X, and excluding portions of the subbox X that violate the set of equality constraints.