- Title
- About extensions of the extremal principle
- Creator
- Bui, Hoa; Kruger, Alexander
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/165499
- Identifier
- vital:13281
- Identifier
-
https://doi.org/10.1007/s10013-018-0278-y
- Identifier
- ISBN:2305-221X
- Abstract
- 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, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.
- Publisher
- Springer Singapore
- Relation
- Vietnam Journal of Mathematics Vol. 46, no. 2 (2018), p. 215-242; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- Copyright © Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Ekeland variational principle; Extremal principle; Extremality; Regularity; Separability; Stationarity; Transversality
- Full Text
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