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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Control and Optimization

ISSN

0363-0129

e-ISSN

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Svazek periodika

53

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

1003-1019

Kód UT WoS článku

000353954300018

EID výsledku v databázi Scopus

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