Solving reachability problems by a scalable constrained optimization method

In this paper we consider the problem of finding an evolution of a dynamical system that originates and terminates in given sets of states. However, if such an evolution exists then it is usually not unique. We investigate this problem and find a scalable approach for solving it. In addition, the resulting saddle-point matrix is sparse. We exploit the structure in order to reach an efficient implementation of our method. In computational experiments we compare line search and trust-region methods as well as various methods for Hessian approximation.