Inexact Newton methods for solving nonsmooth equations

JoséMario Martínez; Liqun Qi

doi:10.1016/0377-0427(94)00088-I

Inexact Newton methods for solving nonsmooth equations

JoséMario Martínez, Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

100 Citations (Scopus)

Abstract

This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We define two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BD-regularity at the solution. We introduce a globally convergent inexact iteration function based method. We discuss implementations and we give some numerical examples.

Original language	English
Pages (from-to)	127-145
Number of pages	19
Journal	Journal of Computational and Applied Mathematics
Volume	60
Issue number	1-2
DOIs	https://doi.org/10.1016/0377-0427(94)00088-I
Publication status	Published - 20 Jun 1995
Externally published	Yes

Keywords

Global convergence
Inexact Newton methods
Nonsmooth analysis
Superlinear convergence

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1016/0377-0427(94)00088-I

Cite this

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AU - Qi, Liqun

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AB - This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We define two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BD-regularity at the solution. We introduce a globally convergent inexact iteration function based method. We discuss implementations and we give some numerical examples.

KW - Global convergence

KW - Inexact Newton methods

KW - Nonsmooth analysis

KW - Superlinear convergence

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DO - 10.1016/0377-0427(94)00088-I

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EP - 145

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IS - 1-2

ER -

Inexact Newton methods for solving nonsmooth equations

Abstract

Keywords

ASJC Scopus subject areas

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