A Newton iteration for differentiable set-valued maps
We employ recent developments of generalized differentiation concepts for set-valued mappings and present a Newton-like iteration for solving generalized equations of the form f(x)+F(x)∋0 where f is a single-valued function while F stands for a set-valued map, both of them being smooth mappings acti...
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Published in | Journal of mathematical analysis and applications Vol. 399; no. 1; pp. 213 - 224 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.03.2013
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | We employ recent developments of generalized differentiation concepts for set-valued mappings and present a Newton-like iteration for solving generalized equations of the form f(x)+F(x)∋0 where f is a single-valued function while F stands for a set-valued map, both of them being smooth mappings acting between two general Banach spaces X and Y. The Newton iteration we propose is constructed on the basis of a linearization of both f and F; we prove that, under suitable assumptions on the “derivatives” of f and F, it converges Q-linearly to a solution to the generalized equation in question. When we strengthen our assumptions, we obtain the Q-quadratic convergence of the method. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/j.jmaa.2012.10.012 |