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Approximate Newton methods for nonsmooth equations

Xu, Huifu and Chang, Xiaowen (1997) Approximate Newton methods for nonsmooth equations Journal of Optimization Theory and Applications, 93, (2), pp. 373-394. (doi:10.1023/A:1022606224224).

Record type: Article


We develop general approximate Newton methods for solving Lipschitz continuous equations by replacing the iteration matrix with a consistently approximated Jacobian, thereby reducing the computation in the generalized Newton method. Locally superlinear convergence results are presented under moderate assumptions. To construct a consistently approximated Jacobian, we introduce two main methods: the classic difference approximation method and the epsi-generalized Jacobian method. The former can be applied to problems with specific structures, while the latter is expected to work well for general problems. Numerical tests show that the two methods are efficient. Finally, a norm-reducing technique for the global convergence of the generalized Newton method is briefly discussed.

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Published date: 1997
Organisations: Operational Research


Local EPrints ID: 79536
ISSN: 0022-3239
PURE UUID: 95ad6b9b-e030-4aea-9cb2-dcb686ce30db

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

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Author: Huifu Xu
Author: Xiaowen Chang

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