Computation of consistent initial values for optimal control problems withDAE systems of higher index

In recent years direct methods have been favored for solving optimal contro l problems with ODE systems. These approaches reduce the "infinite-dimensio nal" optimization problem to a finite-dimensional optimization problem by a pproximating the control and the state over a fixed grid. Because of specia l problems arising from differential-algebraic equation systems (DAE system s), e.g. the calculation of consistent initial values, the transfer of thes e ideas to DAE optimal control problems (DOCP) can not be done without furt her ado. Hence we suggest ideas for a direct solution of DOCP taking these problems into account and present numerical methods for the solution of hig her index systems. A high dimensional example is discussed which shows the efficiency and robustness of the proposed methods.