A reduced space interior point strategy for optimization of differential algebraic systems

Abstract

A novel nonlinear programming (NLP) strategy is developed and applied to the optimization of differential algebraic equation (DAE) systems. Such problems, also referred to as dynamic optimization problems, are common in process engineering and remain challenging applications of nonlinear programming. These applications often consist of large, complex nonlinear models that result from discretizations of DAEs. Variables in the NLP include state and control variables, with far fewer control variables than states. Moreover, all of these discretized variables have associated upper and lower bounds that can be potentially active. To deal with this large, highly constrained problem, an interior point NLP strategy is developed. Here a log barrier function is used to deal with the large number of bound constraints in order to transform the problem to an equality constrained NLP. A modified Newton method is then applied directly to this problem. In addition, this method uses an efficient decomposition of the discretized DAEs and the solution of the Newton step is performed in the reduced space of the independent variables. The resulting approach exploits many of the features of the DAE system and is performed element by element in a forward manner. Several large dynamic process optimization problems are considered to demonstrate the effectiveness of this approach, these include complex separation and reaction processes (including reactive distillation) with several hundred DAEs. NLP formulations with over 55 000 variables are considered. These problems are solved in 5–12 CPU min on small workstations.