On uniform regularity and strong regularity

Kód výsledku v IS VaVaI

RIV/49777513:23520/19:43952543 - isvavai.cz

Výsledek na webu

https://doi.org/10.1080/02331934.2018.1547383

DOI - Digital Object Identifier

10.1080/02331934.2018.1547383

Jazyk výsledku

angličtina

Název v původním jazyce

On uniform regularity and strong regularity

Popis výsledku v původním jazyce

We investigate uniform versions of (metric) regularity and strong (metric) regularity on compact subsets of Banach spaces, in particular, along continuous paths. These two properties turn out to play a key role in analyzing path-following schemes for tracking a solution trajectory of a parametric generalized equation or, more generally, of a differential generalized equation (DGE). The latter model allows us to describe in a unified way several problems in control and optimization such as differential variational inequalities and control systems with state constraints. We study two inexact path-following methods for DGEs having the order of the grid error O(h) and O(h^2), respectively. We provide numerical experiments, comparing the schemes derived, for simple problems arising in physics. Finally, we study metric regularity of mappings associated with a particular case of the DGE arising in control theory. We establish the relationship between the pointwise version of this property and its counterpart in function spaces.

Název v anglickém jazyce

On uniform regularity and strong regularity

Popis výsledku anglicky

We investigate uniform versions of (metric) regularity and strong (metric) regularity on compact subsets of Banach spaces, in particular, along continuous paths. These two properties turn out to play a key role in analyzing path-following schemes for tracking a solution trajectory of a parametric generalized equation or, more generally, of a differential generalized equation (DGE). The latter model allows us to describe in a unified way several problems in control and optimization such as differential variational inequalities and control systems with state constraints. We study two inexact path-following methods for DGEs having the order of the grid error O(h) and O(h^2), respectively. We provide numerical experiments, comparing the schemes derived, for simple problems arising in physics. Finally, we study metric regularity of mappings associated with a particular case of the DGE arising in control theory. We establish the relationship between the pointwise version of this property and its counterpart in function spaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

GA15-00735S: Analýza stability optim a ekvilibrií v ekonomii

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

OPTIMIZATION

ISSN

0233-1934

e-ISSN

—

Svazek periodika

68

Číslo periodika v rámci svazku

2-3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

29

Strana od-do

549-577

Kód UT WoS článku

000462381900008

EID výsledku v databázi Scopus

2-s2.0-85057321614