Fast numerical methods for mixed-integer nonlinear model-predictive control. The author develops and investigates efficient numerical methods for nonlinear mixed-integer optimal control and model-predictive control problems. His thesis presents a lot of novel results and tools in a number of areas. New algorithms based on Bock’s direct multiple shooting method consist of convexification and relaxation techniques and a real-time iteration scheme. A proof of local contractivity under reasonable assumptions is given. The obtained nonlinear programs are treated as mathematical programs with vanishing constraints. The author develops and describes new tools for solving the arising nonconvex quadratic subproblems such as a new parametric active set method based on strong stationarity, a block structured factorization, and new matrix update techniques for this factorization. All developed algorithms are implemented in two software packages MuShROOM and qpHPSC and their efficiency is demonstrated on several applications, especially on a real-time predictive cruise control problem.