We consider a time-dependent optimal control problem, where the state
evolution is described by an ODE. There is a variety of methods for the treatment
of such problems. We prefer to view them as boundary value problems and apply to
them the Riccati approach for non-linear BVPs with separated boundary conditions.
There are many relationships between multiple shooting techniques, the Riccati
approach and the Pantoja method, which describes a computationally efficient
stage-wise construction of the Newton direction for the discrete-time optimal control
problem.
We present an efficient implementation of this approach. Furthermore, the wellknown
checkpointing approach is extended to a `nested checkpointing` for multiple
transversals. Some heuristics are introduced for an efficient construction of nested
reversal schedules. We discuss their benefits and compare their results to the optimal
schedules computed by exhaustive search techniques.