New version of Newton's method for nonsmooth equations

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


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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.

Item Type: Article
ISSNs: 0022-3239 (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 79537
Date Deposited: 17 Mar 2010
Last Modified: 06 Aug 2015 02:59

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