BibTeX
@INCOLLECTION{
Khan2012EaE,
title = "Evaluating an Element of the {C}larke Generalized {J}acobian of a Piecewise
Differentiable Function",
doi = "10.1007/9783642300233_11",
author = "Kamil A. Khan and Paul I. Barton",
abstract = "The (Clarke) generalized Jacobian of a locally Lipschitz continuous function is a
derivativelike setvalued mapping that contains slope information. Several methods for optimization
and equation solving require evaluation of generalized Jacobian elements. However, since the
generalized Jacobian does not satisfy calculus rules sharply, this evaluation can be difficult. In
this work, a method is presented for evaluating generalized Jacobian elements of a nonsmooth
function that is expressed as a finite composition of absolute value functions and continuously
differentiable functions. The method makes use of the principles of automatic differentiation and
the theory of piecewise differentiable functions, and is guaranteed to be computationally tractable
relative to the cost of a function evaluation.",
pages = "115125",
crossref = "Forth2012RAi",
booktitle = "Recent Advances in Algorithmic Differentiation",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
address = "Berlin",
volume = "87",
editor = "Shaun Forth and Paul Hovland and Eric Phipps and Jean Utke and Andrea Walther",
isbn = "9783540689355",
issn = "14397358",
year = "2012",
ad_theotech = "Generalized Jacobian"
}
