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), 373-394. (doi:10.1023/A:1022606224224).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1023/A:1022606224224
ISSNs: 0022-3239 (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 79536
Accepted Date and Publication Date:
Date Deposited: 17 Mar 2010
Last Modified: 31 Mar 2016 13:15

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