- Title
- Error bounds revisited
- Creator
- Cuong, Nguyen; Kruger, Alexander
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185245
- Identifier
- vital:16625
- Identifier
-
https://doi.org/10.1080/02331934.2022.2032695
- Identifier
- ISBN:0233-1934 (ISSN)
- Abstract
- We propose a unifying general framework of quantitative primal and dual sufficient and necessary error bound conditions covering linear and nonlinear, local and global settings. The function is not assumed to possess any particular structure apart from the standard assumptions of lower semicontinuity in the case of sufficient conditions and (in some cases) convexity in the case of necessary conditions. We expose the roles of the assumptions involved in the error bound assertions, in particular, on the underlying space: general metric, normed, Banach or Asplund. Employing special collections of slope operators, we introduce a succinct form of sufficient error bound conditions, which allows one to combine in a single statement several different assertions: nonlocal and local primal space conditions in complete metric spaces, and subdifferential conditions in Banach and Asplund spaces. © 2022 Informa UK Limited, trading as Taylor & Francis Group.
- Publisher
- Taylor and Francis Ltd.
- Relation
- Optimization Vol. 71, no. 4 (2022), p. 1021-1053; https://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 © 2022 Informa UK Limited, trading as Taylor & Francis Group
- Rights
- Open Access
- Subject
- 4901 Applied mathematics; 4903 Numerical and computational mathematics; 49J52; 49J53; 49K40; 90C30; 90C46; Error bound; semi-infinite programming; slope; subdifferential; subregularity
- Full Text
- Reviewed
- Funder
- The research was supported by the Australian Research Council, project DP160100854. 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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