Computational Optimization and Applications

, Volume 62, Issue 1, pp 131–155 | Cite as

Lossy compression for PDE-constrained optimization: adaptive error control

  • Sebastian GötschelEmail author
  • Martin Weiser


For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid solving large systems in the dimension of the full spatio-temporal discretization. The evaluation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results which are accurate enough, in many cases very fine discretizations in time and space are necessary, which leads to a significant amount of data to be stored and transmitted to mass storage. Lossy compression methods were developed to overcome the storage problem by reducing the accuracy of the stored trajectories. The inexact data induces errors in the reduced gradient and reduced Hessian. In this paper, we analyze the influence of such a lossy trajectory compression method on Newton-CG methods for optimal control of parabolic PDEs and design an adaptive strategy for choosing appropriate quantization tolerances.


Optimal control Semi-linear parabolic PDEs Newton-CG Trajectory storage Lossy compression 

Mathematics Subject Classification

35K58 49M15 65M60 68P30 94A29 



The authors gratefully acknowledge support by the DFG Research Center Matheon, project F9.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Zuse Institute BerlinBerlinGermany

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