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"
}