About Extensions of the Extremal Principle
© 2018, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. In this paper, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets, and the corresponding (extended)...
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| Format: | Journal Article |
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Springer
2018
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| Online Access: | http://purl.org/au-research/grants/arc/DP160100854 http://hdl.handle.net/20.500.11937/81341 |
| _version_ | 1848764351191711744 |
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| author | Bui, Hoa Kruger, A.Y. |
| author_facet | Bui, Hoa Kruger, A.Y. |
| author_sort | Bui, Hoa |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2018, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. In this paper, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets, and the corresponding (extended) extremal principle, we focus on extensions of these properties and the corresponding dual conditions with the goal to refine the main arguments used in this type of results, clarify the relationships between different extensions, and expand the applicability of the generalized separation results. We introduce and study new more universal concepts of relative extremality and stationarity and formulate the relative extended extremal principle. Among other things, certain stability of the relative approximate stationarity is proved. Some links are established between the relative extremality and stationarity properties of collections of sets and (the absence of) certain regularity, lower semicontinuity, and Lipschitz-like properties of set-valued mappings. |
| first_indexed | 2025-11-14T11:17:58Z |
| format | Journal Article |
| id | curtin-20.500.11937-81341 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:17:58Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-813412021-03-23T02:47:29Z About Extensions of the Extremal Principle Bui, Hoa Kruger, A.Y. © 2018, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. In this paper, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets, and the corresponding (extended) extremal principle, we focus on extensions of these properties and the corresponding dual conditions with the goal to refine the main arguments used in this type of results, clarify the relationships between different extensions, and expand the applicability of the generalized separation results. We introduce and study new more universal concepts of relative extremality and stationarity and formulate the relative extended extremal principle. Among other things, certain stability of the relative approximate stationarity is proved. Some links are established between the relative extremality and stationarity properties of collections of sets and (the absence of) certain regularity, lower semicontinuity, and Lipschitz-like properties of set-valued mappings. 2018 Journal Article http://hdl.handle.net/20.500.11937/81341 10.1007/s10013-018-0278-y http://purl.org/au-research/grants/arc/DP160100854 Springer fulltext |
| spellingShingle | Bui, Hoa Kruger, A.Y. About Extensions of the Extremal Principle |
| title | About Extensions of the Extremal Principle |
| title_full | About Extensions of the Extremal Principle |
| title_fullStr | About Extensions of the Extremal Principle |
| title_full_unstemmed | About Extensions of the Extremal Principle |
| title_short | About Extensions of the Extremal Principle |
| title_sort | about extensions of the extremal principle |
| url | http://purl.org/au-research/grants/arc/DP160100854 http://hdl.handle.net/20.500.11937/81341 |