Newton methods for solving two classes of nonsmooth equations.
type: Item
instance of: scholarly article
title: Newton methods for solving two classes of nonsmooth equations.
zbMATH Open document ID: 1068.65063
DOI: 10.1023/A:1013791923957
author: Yan Gao
published in: Applications of Mathematics
publication date: 2005-04-19T00:00:00Z
full work available at URL: https://eudml.org/doc/33084
review text: The author considers systems of nonsmooth equations which are formed by max-type functions or by smooth compositions of max-type functions. The modification of the Newton method, proposed by the author, is based on the new definition of the differential for the functions \(F:\mathbb R^n\rightarrow \mathbb R^n.\) This method can be implemented more easily than previous ones because they do not require an element of the Clarke generalized Jacobian [cf. \textit{F. H. Clarke}, Optimization and nonsmooth analysis (1983; Zbl 0582.49001)]. The \(Q\)-superlinear convergence is proved.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 2158707
zbMATH Keywords: nonsmooth equations
zbMATH Keywords: Newton method
zbMATH Keywords: convergence
zbMATH Keywords: max-type functions
zbMATH Keywords: Clarke generalized Jacobian
MaRDI profile type: Publication
cites work: Variational principle with nonlinear complementarity for three-dimensional contact problems and numerical method
cites work: A verification method for solutions of nonsmooth equations
cites work: Optimization and nonsmooth analysis
cites work: Q4246317
cites work: Semismooth and Semiconvex Functions in Constrained Optimization
cites work: Q5652137
cites work: Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
cites work: A nonsmooth version of Newton's method
cites work: Newton and Quasi-Newton Methods for a Class of Nonsmooth Equations and Related Problems
Recommended article: Newton and Quasi-Newton Methods for a Class of Nonsmooth Equations and Related Problems
Recommended article: On Newton's method for solving equations containing nonsmooth operators
Recommended article: Newton's method for a class of nonsmooth functions
Recommended article: On a class of Newton-like methods for solving nonlinear equations
Recommended article: Two new Newton-type methods for the nonlinear equations
Recommended article: Newton methods for solving nonsmooth equations via a new subdifferential
Recommended article: Q4791621
Recommended article: Q5480873
Recommended article: Q4544116
Recommended article: Inexact Newton methods for solving nonsmooth equations
description: scientific article; zbMATH DE number 2158707