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New version of Newton's method for nonsmooth equations

Record type: Article

In this paper, an inexact Newton scheme is presented which produces a sequence of iterates in which the problem functions are differentiable. It is shown that the use of the inexact Newton scheme does not reduce the convergence rate significantly. To improve the algorithm further, we use a classical finite-difference approximation technique in this context. Locally superlinear convergence results are obtained under reasonable assumptions. To globalize the algorithm, we incorporate features designed to improve convergence from an arbitrary starting point. Convergence results are presented under the condition that the generalized Jacobian of the problem function is nonsingular. Finally, implementations are discussed and numerical results are presented.

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Citation

Xu, Huifu and Glover, Barney (1997) New version of Newton's method for nonsmooth equations Journal of Optimization Theory and Applications, 93, (2), pp. 395-414. (doi:10.1023/A:1022658208295).

More information

Published date: 1997
Organisations: Operational Research

Identifiers

Local EPrints ID: 79537
URI: http://eprints.soton.ac.uk/id/eprint/79537
ISSN: 0022-3239
PURE UUID: 81014edc-f673-40ad-9539-320e42f756d1

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Date deposited: 17 Mar 2010
Last modified: 18 Jul 2017 23:17

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Contributors

Author: Huifu Xu
Author: Barney Glover

University divisions

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