Reliable process modelling and optimisation using interval analysis
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Thu, 01/03/2001 14:00 |
Prof Mark Stadtherr (University of Notre Dame) |
Computational Mathematics and Applications  |
Rutherford Appleton Laboratory, nr Didcot |
| 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. | |||