Study On Theory And Algorithm For Large-Scale Nonlinear Process System Optimization

Nonlinear programming (NLP) is an essential tool in process engineering. The advances in computer technology and numerical methods enable engineers to consider more large-scale and complex systems. Emphasis is laid on solving large NLPs efficiently and stably. Reduced-space methods have advantages in process engineering. For one thing, most problems in this category have only few degrees of freedom compared to the total number of variables. For another, reduced-space approaches allow to exploit problem-dependent structure and approximate second derivative information. The objective of this dissertation is the design and implementation of reduced-space algorithms appropriate to large NLPs, especially the strategies necessary for NLP solvers to solve problems stably and balance between computational cost and precision. Properties of the strategies are analysed, and performance of the new solvers is evaluated by tests on a large variety of NLPs.The algorithms discussed include reduced-space SQP (rSQP) and interior point method (rIPOPT). Strategies which can be applied to both of the algorithms are proposed. In order to solve the decomposed system efficiently, an approximate method is introduced, accordingly, the computation order is changed. When solving rank deficient systems, dimension change is necessary for achieving system decomposition and numerical stability. Additionally, checking on rank change and (local) infeasibility during the process of optimization is needed, which can be implemented efficiently by appropriate application of a sparse system solver. Global convergence is guaranteed by feasibility restoration algorithms, i.e. the algorithms based on barrier method and projected gradient method respectively. A robust algorithm without feasibility restoration phase is discussed as well. The trade-off between computational cost and precision is implemented in criteria taking advantage of convergence depth, which try to detect acceptable approximate solution, and discover the proper time to terminate the optimization algorithm.Theoretical discussion includes the solution of barrier feasibility restoration problem corresponding to a rank deficient system, especially an inconsistent system; global convergence and convergence rate of the feasibility restoration algorithm following projected gradient methods; global convergence of the robust algorithm without feasibility restoration phase; and proofs of the properties of convergence criteria based on convergence depth.The practical performance of rSQP algorithm coded in MATLAB as a general purpose NLP solver is tested on various NLP problems from CUTE, COPS, and MITT. The performance is compared with that of MINOS and SNOPT. In the application to process engineering, the advantage of reduced-space methods is demonstrated in the optimization of distillation columns in ethylene production. rIPOPT in FORTRAN performs very well in the solution of rank deficient problems and tests on global convergence and infeasibility identification. The effectiveness of criteria based on convergence depth control is shown by the rSQP algorithm in the solution of problems from CUTE, distillation columns under changing feed conditions, and catalyst mixing problem.