Approximations and Generalized Newton Methods

We study local convergence of generalized Newton methods for both equations and inclusions by using known and new approximations and regularity properties at the solution. Including Kantorovich-type settings, our goal are statements about all (not only some) Newton sequences with appropriate initial points. Our basic tools are results of Klatte-Kummer (2002) and Kummer (1988, 1995), mainly about Newton maps and modified successive approximation, but also graph-approximations of multifunctions and others. Typical examples and simplifications of existing methods are added.


Mathematical Programming Ser. B, accepted version. DOI 10.1007/s10107-017-1194-8 Published online 11 September 2017, the final version is available at



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