Patent ID: 7028065

Claim:
A method for using a computer system to solve a global inequality constrained optimization problem specified by a function f and a set of inequality constraints p j (x)=<0 (i=1, . . . , m), wherein f and p i are scalar functions of a vector x=(x 1 , x 2 , x 3 , . . . x n ), the method comprising: receiving a representation of the function/and the set of inequality constraints at the computer system; storing the representation in a memory within the computer system; performing an interval inequality constrained global optimization process to compute guaranteed bounds on a globally minimum value of the function f(x) subject to the set of inequality constraints; wherein performing the interval global optimization process involves, applying term consistency to the set of inequality constraints over a sub-box X, and excluding any portion of the sub-box X that is proved to be in violation of at least one member of the set of inequality constraints; and recording the guaranteed bounds in the computer system memory; wherein applying term consistency involves: symbolically manipulating an equation within the computer system to solve for a term, g(x′ j ), thereby producing a modified equation g(x′ j )=h(x), wherein the term g(x′ j ) is analytically inverted to produce an inverse function g −1 (y); substituting the sub-box X into the modified equation to produce the equation g(X′ j )=h(X); solving for X′ j with the j-th element of the sub-box X to produce a new sub-box X + ; wherein the nuew sub-box X + contains all solutions of the equation within the sub-box X, and wherein the size of the new sub-box X + is less than or equal to the size of the sub-box X.