Direct discretization methods for optimization boundary value problems in DAE

Practical optimal control problems, e.g., from the areas of robotics or chemical engineering are typically nonlinear and of high dimension. For these problem classes, direct discretization methods have proved to be very eecient and reliable tools. They allow the simultaneous solution of the optimization and the simulation task, therefore reducing the amount of computational eeort considerably. These direct methods use an a-priori discretization of the control functions, e.g., by piecewise polynomials, and of the state functions, e.g., by multiple shooting or col-location. Here, we focus on recent algorithmic developments for the treatment of the resulting large nite dimensional optimization problems. In particular, so-called partially reduced SQP methods are presented as a family of methods including full SQP as well as pure reduced SQP methods. These methods are apt to be tailored speciically to the structures of the problem at hand. Additionally, multilevel control mesh adaptation schemes are explained.