Structure Exploitation in an Interior-Point Method for Fully Discretized, State Constrained Optimal Control Problems

We discuss a direct discretization method for state-constrained optimal control problems and an interior-point method, which is used to solve the resulting large-scale and sparse nonlinear optimization problems. The main focus of the paper is on the investigation of an efficient method to solve the occurring linear equations with saddle-point structure. To this end, we exploit the particular structure that arises from the optimal control problem and the discretization scheme and use a tailored linear algebra solver alglin in combination with a re-ordering of the saddle-point matrices. Numerical experiments for a simple optimal control problem show a significant speed-up compared to state-of-the-art sparse LU decomposition methods like MA57 or MUMPS in combination with Ipopt.