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Approximations and Generalized Newton Methods

Diethard Klatte (diethard.klatte***at***uzh.ch)
Bernd Kummer (kummer***at***math.hu-berlin.de)

Abstract: 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.

Keywords: Generalized Newton method, inclusion, generalized equation, Newton map, successive approximation, graph-approximation, regularity, Kantorovich-Newton method

Category 1: Convex and Nonsmooth Optimization

Category 2: Complementarity and Variational Inequalities

Category 3: Nonlinear Optimization

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

Download: [PDF]

Entry Submitted: 02/24/2016
Entry Accepted: 02/24/2016
Entry Last Modified: 09/27/2017

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