Applying term consistency to an inequality constrained interval global optimization problem

A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for using a computer system to solve a global inequality constrained optimization problem specified by a function ƒ and a set of inequality constraints pi(x)<(i=1, . . . m), wherein ƒ is a scalar function of a vector x=(x1, x2, x3, . . . xn), the method comprising:

• receiving a representation of the function ƒ 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 ƒ(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 subbox X, and
• excluding any portion of the subbox X that is proved to be in violation of at least one member of the set of inequality constraints.

An apparatus for using a computer system to solve a global inequality constrained optimization problem specified by a function ƒ and a set of inequality constraints pi(x)≦0 (i=1, . . . , m), wherein ƒ is a scalar function of a vector x=(x1, x2, x3, . . . . xn), the apparatus comprising:

• a receiving mechanism that is configured to receive a representation of the function ƒ and the set of inequality constraints at the computer system;
• a memory within the computer system for storing the representation;
• a global optimizer that is configured to perform an interval inequality constrained global optimization process to compute guaranteed bounds on a globally minimum value of the function ƒ(x) subject to the set of inequality constraints;
• a term consistency mechanism within the global optimizer that is configured to,
• apply term consistency to the set of inequality constraints over a subbox X, and to
• exclude any portion of the subbox X that is proved to be in violation of at least one member of the set of inequality constraints.