BILEVEL PROGRAMMING FOR STEADY-STATE CHEMICAL PROCESS DESIGN .1. FUNDAMENTALS AND ALGORITHMS

An earlier paper, Clark and Westerberg (Comput. chem. Engng 7, 259-278, 1983) introduced the bilevel programming problem (BLPP), discussed its relevance for the optimization of process models involving thermodynamic equilibrium, and presented the rudiments of two algorithms for locating local optima in the nonlinear case. Since that time, a number of algorithms for the linear and nonlinear BLPP have appeared in the operations research literature. The present article gives a much more complete analysis of the difficult nature of the bilevel program, examines features pertinent to the process design application, reviews the progress in the field since our earlier work, and completes the development of the two algorithms outlined before. We concluded previously that the complexities required to address degenerate points for the inner optimization should favor a problem relaxation over a method using active sets. Here, we demonstrate that the optimization of a process model involving phase equilibrium cannot exhibit this degeneracy, so the active set method should be competitive for this important process design application. Part II of this series compares the performance of the two methods on a process design problem. © 1990.