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Contribution Details
| Type | Conference Presentation |
| Scope | Discipline-based scholarship |
| Title | On Extensions of Newton's Method for Equations and Inclusions |
| Organization Unit | |
| Authors |
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| Presentation Type | lecture |
| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Page Range | 1 - 18 |
| Event Title | Workshop on Nonsmooth and Variational Analysis |
| Event Type | workshop |
| Event Location | Universität Wien |
| Event Start Date | January 28 - 2019 |
| Event End Date | February 1 - 2019 |
| Abstract Text | We present approaches to (generalized) Newton methods in the framework of generalized equations $0\in f(x)+M(x)$, where $f$ is a function and $M$ is a multifunction. The Newton steps are defined by suitable approximations $\hat f$ of $f$ and the solutions of $0\in \hat{f}(x)+M(x)$. We analyze superlinear local convergence analysis of such methods, in particular we extend convergence results via Newton maps from equations to generalized equations both for linear and nonlinear approximations $\hat f$. Moreover, we present relations between semi-smoothness, Newton maps and directional differentiability of $f$. The presentation is based on the following paper: D. Klatte, B. Kummer, ''Approximations and Generalized Newton Methods", Mathematical Programming, Series B, Vol. 168 (2018) 673--716. |
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