On the accurate solution of differential-algebraic optimization problems

Abstract: "Differential-algebraic optimization problems arise often in chemical engineering processes. Current numerical methods for differential-algebraic optimization problems rely on some form of approximation in order to pose the problem as a nonlinear program. Here we explore an appropriate discretization and formulation of this optimization problem by considering stability and error properties of implicit Runge-Kutta (IRK) methods for differential-algebraic equation (DAE) systems. From these properties we are able to enforce appropriate error constraints and method orders in a collocation based nonlinear programming (NLP) formulation.After demonstrating the IRK properties on a small DAE system, we show from variational conditions that optimal control problems can have the same difficulties as higher index DAE systems. This is illustrated for a number of small chemical engineering optimization examples that exhibit higher index characteristics. For these cases the NLP formulation in this paper yields efficient and accurate solutions."