One- and multistep discretizations of index 2 differential algebraic systems and their use in optimization

An approach to solve constrained minimization problems is to integrate a corresponding index 2 differential algebraic equation (DAE). Here, corresponding means that the ω-limit sets of the DAE dynamics are local solutions of the minimization problem. In order to obtain an efficient optimization code, we analyze the behavior of certain Runge–Kutta and linear multistep discretizations applied to these DAEs. It is shown that the discrete dynamics reproduces the geometric properties and the long-time behavior of the continuous system correctly. Finally, we compare the DAE approach with a classical SQP-method.