BibTeX
@ARTICLE{
Kubota2018Eos,
crossref = "Christianson2018Sio",
author = "Koichi Kubota",
title = "Enumeration of subdifferentials of piecewise linear functions with absnormal form",
journal = "Optimization Methods \& Software",
volume = "33",
number = "46",
pages = "11561172",
year = "2018",
publisher = "Taylor \& Francis",
doi = "10.1080/10556788.2018.1458848",
url = "https://doi.org/10.1080/10556788.2018.1458848",
eprint = "https://doi.org/10.1080/10556788.2018.1458848",
abstract = "The directional derivatives of a piecewise smooth function at a given point can be
computed with Griewank's absolute normal form (ANF). When the given point is a
nondifferentiable point, the resulting derivative by ordinary algorithmic differentiation is
included in the subdifferential. In this paper, with ANF, a method for computing and enumerating the
elements of the limiting subdifferential at a given nondifferential point is described with branch
and bound search. Using such an enumeration, we can compute the values of limiting derivatives and,
if required, we can check the firstorder optimality of the piecewise linear function derived by the
piecewise smooth function given by the form of the evaluation procedure, when the sophisticated
algorithm for checking the optimalities is known. The worstcase complexity of the proposed
algorithm is exponential in general, but we show that there may be some cases in which computational
work may be reduced using the branch and bound search with numerical examples.",
booktitle = "Special issue of Optimization Methods \& Software: Advances in
Algorithmic Differentiation",
editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank"
}
