A nonsmooth version of Newton's method

Liqun Qi; Jie Sun

doi:10.1007/BF01581275

A nonsmooth version of Newton's method

Liqun Qi, Jie Sun

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

1208 Citations (Scopus)

Abstract

Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian for C2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.

Original language	English
Pages (from-to)	353-367
Number of pages	15
Journal	Mathematical Programming
Volume	58
Issue number	1-3
DOIs	https://doi.org/10.1007/BF01581275
Publication status	Published - 1 Jan 1993
Externally published	Yes

Keywords

generalized Jacobian
Newton's methods
semismoothness

ASJC Scopus subject areas

Software
General Mathematics

More information

10.1007/BF01581275

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AB - Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian for C2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.

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KW - Newton's methods

KW - semismoothness

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A nonsmooth version of Newton's method

Abstract

Keywords

ASJC Scopus subject areas

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