Abstract

The use of interval methods, in particular interval-Newton/generalized-bisection techniques, provides an approach that is mathematically and computationally guaranteed to reliably solve difficult nonlinear equation solving and global optimization problems, such as those that arise in chemical process modeling. The most significant drawback of the currently used interval methods is the potentially high computational cost that must be paid to obtain the mathematical and computational guarantees of certainty. New methodologies are described here for improving the efficiency of the interval approach. In particular, a new hybrid preconditioning strategy, in which a simple pivoting preconditioner is used in combination with the standard inverse-midpoint method, is presented, as is a new scheme for selection of the real point used in formulating the interval-Newton equation. These techniques can be implemented with relatively little computational overhead, and lead to a large reduction in the number of subintervals that must be tested during the intervalNewton procedure. Tests on a variety of problems arising in chemical process modeling have shown that the new methodologies lead to substantial reductions in computation time requirements, in many cases by multiple orders of magnitude.

Citations