The Radius of Metric Subregularity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00517219" target="_blank" >RIV/67985556:_____/20:00517219 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s11228-019-00523-2" target="_blank" >https://link.springer.com/article/10.1007/s11228-019-00523-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11228-019-00523-2" target="_blank" >10.1007/s11228-019-00523-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Radius of Metric Subregularity

Popis výsledku v původním jazyce

There is a basic paradigm, called here the radius of well-posedness, which quantifies the “distance” from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.

Název v anglickém jazyce

The Radius of Metric Subregularity

Popis výsledku anglicky

There is a basic paradigm, called here the radius of well-posedness, which quantifies the “distance” from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Set-Valued and Variational Analysis

ISSN

1877-0533

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

451-473

Kód UT WoS článku

000554706900002

EID výsledku v databázi Scopus

2-s2.0-85075389144