| This dissertation details the investigation, development and implementation of efficient tools and techniques for optimization of large-scale process problems, in particular those that are characterized by differential and algebraic equation models (DAEs). The basic approach constructs piecewise polynomial approximations to the continuous state profiles of the DAE systems, and discretizes the ordinary differential equations using Orthogonal Collocation on Finite Elements (OCFE). The resulting algebraic system of equations, most often nonlinear, are embedded into the optimization problem, which permits the simultaneous solution and optimization of the process models. The discretized problem is solved with Successive Quadratic Programming (SQP), an efficient nonlinear programming solution technique.; A new decomposition strategy based on Range and Null spaces, RND, is developed and implemented for SQP. This considerably enhances the capabilities of SQP to solve larger, sparse nonlinear problems, and thereby permits the extension of the simultaneous approach outlined above to solve large DAE systems. This decomposition strategy has also been interfaced with GAMS modelling system, which makes convenient process model descriptions and specifications. The efficacy of this package is demonstrated in the solution of a battery of nonlinear programs, including rigorous distillation column simulation and optimization problems.; In discretizing DAE systems on a mesh, the issue of accurate algebraic representation of the original differential equation models is addressed. Criteria which give an accurate estimate of the local truncation error in this approximation are developed from theoretical considerations. They are imposed as a set of constraints in the discretized nonlinear problem, and permit an assessment of the validity of the results obtained. An efficient strategy is then developed to ensure the minimization of the approximation error, by adaptively adjusting both the numbers and the spans of finite elements in the mesh on which the discretized problem is solved.; The effectiveness of the collocation-based simultaneous solution approach and the adaptive mesh refinement strategies is demonstrated with the help of process optimization example problems. These examples require determination of continuous, possibly constrained state profiles, as well as optimal parameter values. |
