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Multistage approaches for optimal offline checkpointing. (English) Zbl 1194.65084
Optimal control problems with time dependent partial differential equations are characterized by the solution of the state equation forward in time and by the solution of the adjoint equation backward in time. This requires for two and three dimensional problems due to size of the discretized problem as well as its nonlinear character a very large number of memory allocations, which forms a main bottleneck in the overall optimization process. For this reason, several checkpointing techniques have been developed.
There are two main checkpointing strategies. In the case of online checkpointing, the number of time steps to be performed is not known a priori. If the number of time steps is known, one uses offline checkpointing strategies. In both approaches, all the checkpoints are kept in the main memory and access time to the checkpoints is negligible, which is called single-stage checkpointing.
The authors consider the situation when parallel input/output devices are used to store the checkpoints, known as multistage checkpointing. In this case the access cost of the checkpoint is no more negligible. In order to minimize the overall access cost to the checkpoints, the write and read counts for each checkpoint in the binomial checkpointing approach are investigated. Numerical results illustrate that the derived checkpointing strategy may reduce the overall computing time.

MSC:
65K10 Numerical optimization and variational techniques
65Y20 Complexity and performance of numerical algorithms
49N90 Applications of optimal control and differential games
68W40 Analysis of algorithms
49J20 Existence theories for optimal control problems involving partial differential equations
Software:
ADOL-C; CompAD; NAGWare
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