Applying term consistency to the solution of unconstrained interval global optimization problems

摘要

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