Inexact Newton Methods and Dennis-Moré Theorems for Nonsmooth Generalized Equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F15%3A43925257" target="_blank" >RIV/49777513:23520/15:43925257 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/140969476" target="_blank" >http://dx.doi.org/10.1137/140969476</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/140969476" target="_blank" >10.1137/140969476</a>

Result language
angličtina
Original language name
Inexact Newton Methods and Dennis-Moré Theorems for Nonsmooth Generalized Equations
Original language description
In this paper we study local convergence of inexact Newton methods for solving the generalized equation in Banach spaces, where the single-valued part f is continuous but not necessarily smooth and the mulivalued part F is a mapping with closed graph. Weutilize conditions divided into three groups: the first concerns the kind of nonsmoothness of f, the second involves metric regularity properties of an approximation of the mapping f+F, and the third is about the sequence of mappings representing inexactness. Under various combinations of these conditions we show linear, superlinear or quadratic convergence of the method. In the second part of the paper we give two generalizations of the Dennis-Moré theorem. As corollaries, we obtain results regardingconvergence of inexact semismooth quasi-Newton type methods and Dennis-Moré theorems for semismooth equations.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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