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Using Automatic Differentiation for Second-Order Matrix-free Methods in PDE-constrained Optimization

  • David E. Keyes
  • Paul D. Hovland
  • Lois C. McInnes
  • Widodo Samyono
Chapter
  • 319 Downloads

Abstract

Classical methods of constrained optimization are often based on the assumptions that projection onto the constraint manifold is routine, but accessing second-derivative information is not. Both assumptions need revision for the application of optimization to systems constrained by partial differential equations, in the contemporary limit of millions of state variables and in the parallel setting. Large-scale PDE solvers are complex pieces of software that exploit detailed knowledge of architecture and application and cannot easily be modified to fit the interface requirements of a black box optimizer. Furthermore, in view of the expense of PDE analyses, optimization methods not using second derivatives may require too many iterations to be practical. For general problems, automatic differentiation is likely to be the most convenient means of exploiting second derivatives. We delineate a role for automatic differentiation in matrix-free optimization formulations involving Newton’s method, in which little more storage is required than that for the analysis code alone.

Keywords

Chromatic Number Full System Automatic Differentiation Schwarz Method Approximate Inverse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • David E. Keyes
  • Paul D. Hovland
  • Lois C. McInnes
  • Widodo Samyono

There are no affiliations available

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