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Newton methods for solving two classes of nonsmooth equations. (English) Zbl 1068.65063
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 \(F:\mathbb R^n\rightarrow \mathbb R^n.\) This method can be implemented more easily than previous ones because they do not require an element of the Clarke generalized Jacobian [cf. F. H. Clarke, Optimization and nonsmooth analysis (1983; Zbl 0582.49001)]. The \(Q\)-superlinear convergence is proved.
Reviewer: Jan Zítko (Praha)

65H10 Numerical computation of solutions to systems of equations
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