Newton methods for solving two classes of nonsmooth equations

Gao, Yan. "Newton methods for solving two classes of nonsmooth equations." Applications of Mathematics 46.3 (2001): 215-229. <http://eudml.org/doc/33084>.

@article{Gao2001,
abstract = {The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not require an element of Clarke generalized Jacobian, of B-differential, or of b-differential, at each iteration point.},
author = {Gao, Yan},
journal = {Applications of Mathematics},
keywords = {nonsmooth equations; Newton method; approximate Newton method; max-type function; composite function; convergence; nonsmooth equations; Newton method; convergence; max-type functions; Clarke generalized Jacobian},
language = {eng},
number = {3},
pages = {215-229},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Newton methods for solving two classes of nonsmooth equations},
url = {http://eudml.org/doc/33084},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Gao, Yan
TI - Newton methods for solving two classes of nonsmooth equations
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 3
SP - 215
EP - 229
AB - The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not require an element of Clarke generalized Jacobian, of B-differential, or of b-differential, at each iteration point.
LA - eng
KW - nonsmooth equations; Newton method; approximate Newton method; max-type function; composite function; convergence; nonsmooth equations; Newton method; convergence; max-type functions; Clarke generalized Jacobian
UR - http://eudml.org/doc/33084
ER -