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Newton’s method based on generalized derivatives for nonsmooth functions: Convergence analysis. (English) Zbl 0768.49012
Advances in optimization, Proc. 6th Fr.-Ger. Colloq., Lambrecht/Ger. 1991, Lect. Notes Econ. Math. Syst. 382, 171-194 (1992).
[For the entire collection see Zbl 0746.00073.]
The paper is devoted to the Newton’s method of solving nonlinear equations $$f(x)=0$$, where $$f:X\to Y$$ and $$X,Y$$ are normed spaces. For nonsmooth functions $$f$$ the problem of convergence of the method is considered with the use of various types of generalized derivatives. The solvability of subproblems — corresponding to one step in the method – - is shown to be a consequence of surjectivity of those derivatives.

MSC:
 49J52 Nonsmooth analysis