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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.

49J52 Nonsmooth analysis