Applying term consistency to an equality constrained interval global optimization problem

A computer-readable storage medium storing instructions that when executed by a computer system cause the computer system to perform a method for using a computer system to solve a global optimization problem specified by a function | and a set of equality constraints, the method comprising:

• receiving a representation of the function | and the set of equality constraints q1(x)=0 (i=1, . . . , r) at the computer system, wherein | is a scalar function of a vector x=(x1, x2, x3, . . . xn);
• storing the representation in a memory within the computer system;
• performing an interval global optimization process to compute guaranteed bounds on a globally minimum vale of the function |(x) subject to the set of equality constraints;
• wherein performing the interval global optimization process involves,
• applying term consistency to the set of equality constraints over a subbox X, and
• excluding portions of the subbox X that can be shown to violate any of the equality constraints

An apparatus that solves a global optimization problem specified by a function | and a set of equality constraints, the apparatus comprising:

• a receiving mechanism that is configured to receive a representation of the function | and the set of equality constraints q1(x)=0 (i=1, . . . , r), wherein | is a scalar function of a vector x=(x1, x2, x3, . . . xn);
• a memory for storing the representation;
• an optimizer that is configured to perform an interval global optimization process to compute guaranteed bounds on a globally minimum value of the function |(x) subject to the set of equality constraints;
• wherein the optimizer is configured to,
• apply term consistency to the set of equality constraints over a subbox X, and to
• exclude portions of the subbox X that can be shown to violate any of the equality constraints