  We present Newton-Krylov methods for efficient numerical solution of optimal
control problems arising in model predictive control, where the optimal control
is discontinuous. As in our earlier work, preconditioned GMRES practically
results in an optimal $O(N)$ complexity, where $N$ is a discrete horizon
length. Effects of a warm-start, shifting along the predictive horizon, are
numerically investigated. The~method is tested on a classical double integrator
example of a minimum-time problem with a known bang-bang optimal control.
