- Title
- Necessary conditions for non-intersection of collections of sets
- Creator
- Bui, Hoa; Kruger, Alexander
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/184746
- Identifier
- vital:16564
- Identifier
-
https://doi.org/10.1080/02331934.2021.1901899
- Identifier
- ISBN:0233-1934 (ISSN)
- Abstract
- This paper continues studies of non-intersection properties of finite collections of sets initiated 40 years ago by the extremal principle. We study elementary non-intersection properties of collections of sets, making the core of the conventional definitions of extremality and stationarity. In the setting of general Banach/Asplund spaces, we establish new primal (slope) and dual (generalized separation) necessary conditions for these non-intersection properties. The results are applied to convergence analysis of alternating projections. © 2021 Informa UK Limited, trading as Taylor & Francis Group.
- Publisher
- Taylor and Francis Ltd.
- Relation
- Optimization Vol. 71, no. 1 (2022), p. 165-196; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2021 Informa UK Limited, trading as Taylor & Francis Group
- Rights
- Open Access
- Subject
- 4901 Applied mathematics; 4903 Numerical and computational mathematics; 49J52; 49J53; 49K40; 90C30; alternating projections; Extremal principle; Regularity; Separation; Transversality
- Full Text
- Reviewed
- Funder
- The research was supported by the Australian Research Council, project DP160100854. The first author is supported by the Australian Research Council through the Centre for Transforming Maintenance through Data Science, project IC180100030. The second author benefited from the support of the European Union's Horizon 2020 research and innovation programme under the Marie Sk
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