Publication: Tangent-on-Tangent vs. Tangent-on-Reverse for Second Differentiation of Constrained Functionals
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Tangent-on-Tangent vs. Tangent-on-Reverse for Second Differentiation of Constrained Functionals

- incollection -
 

Author(s)
Massimiliano Martinelli , Laurent HascoŽt

Published in
Advances in Automatic Differentiation

Editor(s)
Christian H. Bischof, H. Martin Bücker, Paul D. Hovland, Uwe Naumann, J. Utke

Year
2008

Publisher
Springer

Abstract
We compare the Tangent-on-Tangent and the Tangent-on-Reverse strategies to build programs that compute second derivatives (a Hessian matrix) using automatic differentiation. In the specific case of a constrained functional, we find that Tangent-on-Reverse outperforms Tangent-on-Tangent only above a relatively high number of input parameters. We describe the algorithms to help the end-user apply the two strategies to a given application source. We discuss the modification needed inside the automatic differentiation tool to improve Tangent-on-Reverse differentiation.

Cross-References
Bischof2008AiA

AD Tools
TAPENADE

AD Theory and Techniques
Hessian

BibTeX
@INCOLLECTION{
         Martinelli2008ToT,
       title = "Tangent-on-Tangent vs. Tangent-on-Reverse for Second Differentiation of Constrained
         Functionals",
       doi = "10.1007/978-3-540-68942-3_14",
       author = "Massimiliano Martinelli and Laurent Hasco{\"e}t",
       abstract = "We compare the Tangent-on-Tangent and the Tangent-on-Reverse strategies to build
         programs that compute second derivatives (a Hessian matrix) using automatic differentiation. In the
         specific case of a constrained functional, we find that Tangent-on-Reverse outperforms
         Tangent-on-Tangent only above a relatively high number of input parameters. We describe the
         algorithms to help the end-user apply the two strategies to a given application source. We discuss
         the modification needed inside the automatic differentiation tool to improve Tangent-on-Reverse
         differentiation.",
       crossref = "Bischof2008AiA",
       pages = "151--161",
       booktitle = "Advances in Automatic Differentiation",
       publisher = "Springer",
       editor = "Christian H. Bischof and H. Martin B{\"u}cker and Paul D. Hovland and Uwe
         Naumann and J. Utke",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2008",
       ad_tools = "TAPENADE",
       ad_theotech = "Hessian"
}


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