Publication: Reduction of Storage Requirement by Checkpointing for Time-dependent Optimal Control Problems in ODEs
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Reduction of Storage Requirement by Checkpointing for Time-dependent Optimal Control Problems in ODEs

- incollection -
 

Area
Optimal Control

Author(s)
Julia Sternberg , Andreas Griewank

Published in
Automatic Differentiation: Applications, Theory, and Implementations

Editor(s)
H. Martin Bücker, George F. Corliss, Paul D. Hovland, Uwe Naumann, Boyana Norris

Year
2005

Publisher
Springer

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.

Cross-References
Bucker2005ADA

AD Theory and Techniques
Checkpointing

BibTeX
@INCOLLECTION{
         Sternberg2005RoS,
       author = "Julia Sternberg and Andreas Griewank",
       title = "Reduction of Storage Requirement by Checkpointing for Time-dependent Optimal Control
         Problems in {ODE}s",
       pages = "99--110",
       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.",
       crossref = "Bucker2005ADA",
       booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
       year = "2005",
       editor = "H. Martin B{\"u}cker and George F. Corliss and Paul D. Hovland and Uwe
         Naumann and Boyana Norris",
       publisher = "Springer",
       ad_area = "Optimal Control",
       ad_theotech = "Checkpointing",
       doi = "10.1007/3-540-28438-9_9"
}


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