Reduction of Storage Requirement by Checkpointing for Time-Dependent Optimal Control Problems in ODEs

Abstract

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 well-known 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.