article

A nonsmooth version of Newton's method

Authors:

Jie SunAuthors Info & Claims

Mathematical Programming: Series A and B, Volume 58, Issue 1-3

Pages 353 - 367

Published: 01 January 1993 Publication History

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 forC2-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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Index Terms

A nonsmooth version of Newton's method
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
    2. Nonlinear equations
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization

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cover image Mathematical Programming: Series A and B

Mathematical Programming: Series A and B Volume 58, Issue 1-3

January 1993

426 pages

ISSN:0025-5610

Issue’s Table of Contents

Copyright © Copyright © 1993 The Mathematical Programming Society, Inc.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 January 1993

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