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On uniform regularity and strong regularity
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 ge...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Taylor & Francis
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6474740/ https://www.ncbi.nlm.nih.gov/pubmed/31057306 http://dx.doi.org/10.1080/02331934.2018.1547383 |
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author | Cibulka, R. Preininger, J. Roubal, T. |
author_facet | Cibulka, R. Preininger, J. Roubal, T. |
author_sort | Cibulka, R. |
collection | PubMed |
description | 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 [Image: see text] and [Image: see text] , 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. |
format | Online Article Text |
id | pubmed-6474740 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Taylor & Francis |
record_format | MEDLINE/PubMed |
spelling | pubmed-64747402019-05-01 On uniform regularity and strong regularity Cibulka, R. Preininger, J. Roubal, T. Optimization Article 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 [Image: see text] and [Image: see text] , 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. Taylor & Francis 2018-11-19 /pmc/articles/PMC6474740/ /pubmed/31057306 http://dx.doi.org/10.1080/02331934.2018.1547383 Text en © 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group http://creativecommons.org/licenses/by/4.0/ This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Article Cibulka, R. Preininger, J. Roubal, T. On uniform regularity and strong regularity |
title | On uniform regularity and strong regularity |
title_full | On uniform regularity and strong regularity |
title_fullStr | On uniform regularity and strong regularity |
title_full_unstemmed | On uniform regularity and strong regularity |
title_short | On uniform regularity and strong regularity |
title_sort | on uniform regularity and strong regularity |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6474740/ https://www.ncbi.nlm.nih.gov/pubmed/31057306 http://dx.doi.org/10.1080/02331934.2018.1547383 |
work_keys_str_mv | AT cibulkar onuniformregularityandstrongregularity AT preiningerj onuniformregularityandstrongregularity AT roubalt onuniformregularityandstrongregularity |