One embodiment of the present invention provides a system that solves an unconstrained interval global optimization problem specified by a function , wherein is a scalar function of a vector x=(x1, x2, x3, . . . xn). The system operates by receiving a representation of the function , and then performing an interval global optimization process to compute guaranteed bounds on a globally minimum value * of the function (x) and the location or locations x* of the global minimum. While performing the interval global optimization process, the system deletes all of part of a subbox X for which (x)_bar, wherein _bar is the least upper bound on * that has been so far found. This is called the "_bar test". The system applies term consistency to the _bar test over the subbox X to increase that portion of the subbox X that can be proved to violate the _bar test.

 
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