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

Massimiliano Martinelli Laurent Hascoët (INRIA, BP93, 06902 Sophia-Antipolis, France)

Proceedings of the AD2008 Conference, Bonn, Germany, august 2008 (10 pages)

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 AD tool to improve Tangent-on-Reverse AD.

Keywords: Automatic Differentiation, Gradient, Hessian, Tangent-on-Tangent, Tangent-on-Reverse, Software Tools, TAPENADE

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@inproceedings{MartinelliHascoet08,
  author = {Martinelli, M. and Hasco\"et, L.},
  title = {{T}angent-on-{T}angent vs. {T}angent-on-{R}everse for second differentiation of constrained functionals},
  booktitle = {Advances in Automatic Differentiation},
  series = "Lecture Notes in Computational Science and Engineering",
  note = "Selected papers from AD2008 Bonn, August 2008",
  publisher = "Springer",
  pages = "151-162",
  year = 2008
}