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Zbl 1068.65063
Gao, Yan
Newton methods for solving two classes of nonsmooth equations. (English)
[J] Appl. Math., Praha 46, No. 3, 215-229 (2001). ISSN 0862-7940; ISSN 1572-9109/e

The author considers systems of nonsmooth equations which are formed by max-type functions or by smooth compositions of max-type functions. The modification of the Newton method, proposed by the author, is based on the new definition of the differential for the functions $F:\Bbb R^n\rightarrow \Bbb R^n.$ This method can be implemented more easily than previous ones because they do not require an element of the Clarke generalized Jacobian [cf. {\it F. H. Clarke}, Optimization and nonsmooth analysis (1983; Zbl 0582.49001)]. The $Q$-superlinear convergence is proved.
[Jan Z\'{i}tko (Praha)]

MSC 2000:: *65H10 Systems of nonlinear equations (numerical methods)

Keywords: nonsmooth equations; Newton method; convergence; max-type functions; Clarke generalized Jacobian

Citations: Zbl 0582.49001

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