Publication: On the Iterative Solution of Adjoint Equations
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On the Iterative Solution of Adjoint Equations

- incollection -
 

Author(s)
Michael B. Giles

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
This paper considers the iterative solution of the adjoint equations which arise in the context of design optimisation. It is shown that naive adjoining of the iterative solution of the original linearised equations results in an adjoint code which cannot be interpreted as an iterative solution of the adjoint equations. However, this can be achieved through appropriate algebraic manipulations. This is important in design optimisation because one can reduce the computational cost by starting the adjoint iteration from the adjoint solution obtained in the previous design step.

Cross-References
Corliss2002ADo

AD Theory and Techniques
Adjoint, Fixpoint, Reverse Mode

BibTeX
@INCOLLECTION{
         Giles2002OtI,
       author = "Michael B. Giles",
       title = "On the Iterative Solution of Adjoint Equations",
       pages = "145--151",
       chapter = "16",
       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 = "This paper considers the iterative solution of the adjoint equations which arise in
         the context of design optimisation. It is shown that naive adjoining of the iterative solution of
         the original linearised equations results in an adjoint code which cannot be interpreted as an
         iterative solution of the adjoint equations. However, this can be achieved through appropriate
         algebraic manipulations. This is important in design optimisation because one can reduce the
         computational cost by starting the adjoint iteration from the adjoint solution obtained in the
         previous design step.",
       referred = "[Klein2002DMf]",
       ad_theotech = "Adjoint, Fixpoint, Reverse Mode"
}


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