New version of Newton's method for nonsmooth equations
New version of Newton's method for nonsmooth equations
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.
395-414
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Glover, Barney
97b93632-9ebb-444b-9f3a-02a43a78110b
1997
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Glover, Barney
97b93632-9ebb-444b-9f3a-02a43a78110b
Xu, Huifu and Glover, Barney
(1997)
New version of Newton's method for nonsmooth equations.
Journal of Optimization Theory and Applications, 93 (2), .
(doi:10.1023/A:1022658208295).
Abstract
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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Published date: 1997
Organisations:
Operational Research
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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: 14 Mar 2024 02:47
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Author:
Huifu Xu
Author:
Barney Glover
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