- Title
- Transversality properties : primal sufficient conditions
- Creator
- Cuong, Nguyen; Kruger, Alexander
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/176619
- Identifier
- vital:15143
- Identifier
-
https://doi.org/10.1007/s11228-020-00545-1
- Identifier
- ISBN:0927-6947 (ISSN)
- Abstract
- The paper studies ‘good arrangements’ (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric and slope) characterizations of transversality properties in the nonlinear setting. The Hölder case is given a special attention. Our main objective is not formally extending our earlier results from the Hölder to a more general nonlinear setting, but rather to develop a general framework for quantitative analysis of transversality properties. The nonlinearity is just a simple setting, which allows us to unify the existing results on the topic. Unlike the well-studied subtransversality property, not many characterizations of the other two important properties: semitransversality and transversality have been known even in the linear case. Quantitative relations between nonlinear transversality properties and the corresponding regularity properties of set-valued mappings as well as nonlinear extensions of the new transversality properties of a set-valued mapping to a set in the range space due to Ioffe are also discussed. © 2020, Springer Nature B.V.
- Publisher
- Springer Science and Business Media B.V.
- Relation
- Set-Valued and Variational Analysis Vol. 29, no. 2 (2021), p. 221-256; 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 © Springer Nature B.V. 2020
- Rights
- Open Access
- Subject
- 0101 Pure Mathematics; Chain rule; Regularity; Semiregularity; Semitransversality; Slope; Subregularity; Subtransversality; Transversality
- Full Text
- Reviewed
- Funder
- The research was supported by the Australian Research Council, project DP160100854. The second author benefited from the support of the FMJH Program PGMO and from the support of EDF. Acknowledgments
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