Publication: Using Automatic Differentiation for Second-order Matrix-free Methods in PDE-Constrained Optimization
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Using Automatic Differentiation for Second-order Matrix-free Methods in PDE-Constrained Optimization

- incollection -
 

Author(s)
David E. Keyes , Paul D. Hovland , Lois C. McInnes , Widodo Samyono

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

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 blackbox 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.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Keyes2002UAD,
       author = "David E. Keyes and Paul D. Hovland and Lois C. McInnes and Widodo Samyono",
       title = "Using Automatic Differentiation for Second-order Matrix-free Methods in
         {PDE}-Constrained Optimization",
       pages = "35--50",
       chapter = "3",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       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 blackbox 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.",
       referred = "[More2002ADT]."
}


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