Continuing advances in computing technology provide the power not only to solve
increasingly large and complex process modeling and optimization problems, but also
to address issues concerning the reliability with which such problems can be solved.
For example, in solving process optimization problems, a persistent issue
concerning reliability is whether or not a global, as opposed to local,
optimum has been achieved. In modeling problems, especially with the
use of complex nonlinear models, the issue of whether a solution is unique
is of concern, and if no solution is found numerically, of whether there
actually exists a solution to the posed problem. This presentation
focuses on an approach, based on interval mathematics,
that is capable of dealing with these issues, and which
can provide mathematical and computational guarantees of reliability.
That is, the technique is guaranteed to find all solutions to nonlinear
equation solving problems and to find the global optimum in nonlinear
optimization problems. The methodology is demonstrated using several
examples, drawn primarily from the modeling of phase behavior, the
estimation of parameters in models, and the modeling, using lattice
density-functional theory, of phase transitions in nanoporous materials.