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 presented, 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.
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