Publication: Automatic Differentiation of Conditional Branches in an Operator Overloading Context
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Automatic Differentiation of Conditional Branches in an Operator Overloading Context

- incollection -
 

Author(s)
R. Baker Kearfott

Published in
Computational Differentiation: Techniques, Applications, and Tools

Editor(s)
Martin Berz, Christian Bischof, George Corliss, Andreas Griewank

Year
1996

Publisher
SIAM

Abstract
In the past, it has been problematical to include IF-THEN-ELSE branches in automatic differentiation processes driven by operator overloading and code list generation, when the branch condition contains variables. However, this problem can be circumvented with a special ``branch function″ χ. Definition of this function, formulas for its use, and implications of its use will be discussed. A second issue is: what can be done when derivatives are discontinuous? In fact, simple and meaningful Newton iterations can be set up when even the function itself is discontinuous. Simplified figures and examples are given, as well as references to in-depth explanations. An example of the convergence behavior is given with an interval Newton method to find critical points for the problem ``min |x|.″

Cross-References
Berz1996CDT

BibTeX
@INCOLLECTION{
         Kearfott1996ADo,
       author = "R. Baker Kearfott",
       editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
       title = "Automatic Differentiation of Conditional Branches in an Operator Overloading Context",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "75--81",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Kearfott1996ADo",
       crossref = "Berz1996CDT",
       abstract = "In the past, it has been problematical to include {\tt IF-THEN-ELSE} branches
         in automatic differentiation processes driven by operator overloading and code list generation, when
         the branch condition contains variables. However, this problem can be circumvented with a special
         ``branch function'' $\chi$. Definition of this function, formulas for its use, and
         implications of its use will be discussed. A second issue is: what can be done when derivatives are
         discontinuous? In fact, simple and meaningful Newton iterations can be set up when even the function
         itself is discontinuous. Simplified figures and examples are given, as well as references to
         in-depth explanations. An example of the convergence behavior is given with an interval Newton
         method to find critical points for the problem ``$\min |x|$.''",
       keywords = "Conditional branches, operator overloading, branch function, discontinuous
         derivatives.",
       referred = "[Berz2002TaU], [Dignath2002AAa].",
       year = "1996"
}


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