Patent ID: 6922713

Claim:
A method for using a computer system to solve an unconstrained interval global optimization problem specified by a function ƒ, wherein ƒ is a scalar function of a vector x=(x 1 , x 2 , x 3 , . . . x n ), the method comprising: receiving a representation of the function ƒ 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 ƒ(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 ƒ 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 ƒ 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 ƒ(x) using interval arithmetic; and recording the guaranteed bounds in the memory within the computer system.