Reformulating ill-conditioned DAE optimization problems

Abstract: "This paper discusses numerical issues in Differential- Algebraic Equation (DAE) optimization concerning the stability and accuracy of the discretized Nonlinear Programming Problems (NLP). First, a brief description of the solution strategy based on reduced-Hessian Successive Quadratic Programming (rSQP) is described, focusing on the decomposition step of the DAE constraints. Next, some difficulties associated with unstable DAE problem formulations are exposed via examples. A new procedure for detecting ill-conditioning and problem reformulation is then presented. Furthermore, some properties of this procedure as well as its limitations are also discussed. Numerical examples are provided, including a flowsheet optimization problem with an unstable reactor."