Numerical Methods for Parametric Nonlinear Programming and Their Application to the Optimization of a Chemical Process

Optimization problems arise in both the design and operation of chemical processes. However, these problems are often highly uncertain, containing both uncertain model parameters and variable input values (such as upstream flow rates and compositions). Numerous methods have been proposed to handle such uncertainty explicitly, including variants of sensitivity analysis, robust optimization, stochastic optimization and multi-level programming. In addition, several real-time optimization methods have been proposed for steady-state and dynamic plants, where current plant measurements are used to recalculate or update the original optimal solution.

Another approach to optimization under uncertainty is parametric optimization?approximating the optimal solution as a function of the uncertain parameters. This technique is well developed in the linear programming and integer programming literature. However, for nonlinear programming, the methods and codes have been limited to the single parameter case.

This poster presents numerical methods for parametric nonlinear programming with an arbitrary number of uncertain parameters. An example problem based on implicit optimization (a real-time optimization method in which a qualitative optimal solution is identified and subsequently implemented using control techniques) is included as well. Aspects of this work have already been published and/or presented in the following venues:

Hale, Elaine T. Numerical methods for d-parametric nonlinear programming with chemical process control and optimization applications. Ph.D. thesis, University of Texas at Austin, 2005.

Hale, Elaine T. and S. Joe Qin. ?Multi-parametric nonlinear programming and the evaluation of implicit optimization model adequacy.? In Proceedings of the 7th International Symposium on the Dynamics and Control of Process Systems, Cambridge, MA, July 5-8, 2004.

In addition, a related talk will be given at this meeting:

Hale, Elaine T. and S. Joe Qin. ?Nonlinear MPC using multi-parametric nonlinear programming solutions.? To be presented at the American Institute for Chemical Engineers 2005 Annual Meeting, November 3, 2005.