Newton methods for solving two classes of nonsmooth equations. (Q1771826)

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. \textit{F. H. Clarke}, Optimization and nonsmooth analysis (1983; Zbl 0582.49001)]. The \(Q\)-superlinear convergence is proved.