The application of optimization algorithms to high -dimensional nonlinear systems.

摘要

The research described herein consists of two parts. The first part is optimal control. Here, an optimal control algorithm is applied to reactions in a plug flow reactor. Heat and mass fluxes along the side of the reactor are optimized to maximize the yields of desired products and minimize the yields of the unwanted products. Illustrations provided include the optimization of acetylene and ethylene yields in the conversion of methane, minimization of polydisperity and reaction time in polymerization systems, and optimization of formaldehyde yield in homogeneous and catalyzed methanol conversion.;The second part of the research is the use of the technique of High Dimensional Model Representation (HDMR). This technique is used to model input-output mappings. In particular, a Random Sampling HDMR (RS-HDMR) is developed that is computationally efficient for high dimensional problems. The RS-HDMR is applied to the pricing of derivative securities. It is demonstrated that RS-HDMR successfully maps several parameters to the derivative pricing. It is also used in conjunction with the optimal control methodology in sensitivity analysis of a system whose parameters are characterized by large uncertainties.;Part I of this thesis presents the formalism of the optimal control methodology as well as its applications. Part II deals with the HDMR work and its application to derivative pricing and sensitivity analysis.