Abstract

We present here an investigation of strategies for reliable global optimization and nonlinear equation solving using interval analysis. Realistic mathematical modeling in chemical engineering frequently involves nonlinear models, such as thermodynamic equilibrium problems. A rigorous approach for reliably finding all solutions to a system of nonlinear equations or computing globally optimal solutions to nonconvex nonlinear problems is interval analysis, which can provides a mathematical and computational guarantee to the problems. ;High performance computing strategies are presented including component-wise bisection methods and component-wise interval Newton methods to improve the performance of interval analysis. An interval arithmetic library and automatic differentiation library are developed to provide the convenience of interval analysis. An efficient control of the dependency problem based on Taylor polynomial methods, Berz-Taylor model, is investigated, also a Berz-Taylor model library is developed. Computational results are provided for a number of chemical engineering problems as well as for problems taken from the literature. These results indicate that the performance strategies are very effective