Issues in Local Chemical Process Optimization

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Theoretically sound and reasonably reliable and efficient computer tools for finding local solutions to small chemical process optimization problems are currently available. The selection of a suitable method is based on the problem at hand, how it is formulated, the imposed constraints, etc. Successive quadratic programming (SQP) is a good iterative method for solving small nonlinearly constrained optimization problems. For large problems, use of SQP requires either decomposition or clever exploitation of the problem structure. In this project, the PI plans to develop generalizable techniques for using SQP methods to solve large and small chemical process optimization problems with nonlinear constraints (an example of such problems are separation units such as distillation columns). The research will be divided into the following areas: (1) The development of a new method for quadratic programming (QP) based on an active set strategy and a symmetric, indefinite factorization. (2) The development of asymmetric trust region methods for improving the reliability of Newton-like methods. (3) The comparative evaluation of current methods for approximating the Hessian matrix of the Lagrangian function, the development of any new quasi-Newton methods for use in hybrid methods, and a study of the impact of indefinite projected Hessian matrices. (4) The study of the feasibility of automatically generating reliable initial estimates of the unknown variables and multipliers using generic problem information, physical insight, short cut techniques, analysis and/or simulation tools. (5) The numerical implementation and thorough testing of above concepts on a wide variety of relevant small and large- scale chemical process optimization problems.