- Title
- The radius of metric subregularity
- Creator
- Dontchev, Asen; Gfrerer, Helmut; Kruger, Alexander; Outrata, Jiri
- Date
- 2020
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/173307
- Identifier
- vital:14649
- Identifier
-
https://doi.org/10.1007/s11228-019-00523-2
- Identifier
- ISBN:0927-6947 (ISSN)
- Abstract
- There is a basic paradigm, called here the radius of well-posedness, which quantifies the “distance” from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings. © 2019, Springer Nature B.V.; Funding details: Austrian Science Fund, FWF, P26132-N25, P26640-N25, P29190-N32 Funding details: National Science Foundation, NSF Funding details: Australian Research Council, ARC Funding details: Australian Research Council, ARC, DP160100854 Funding details: Austrian Science Fund, FWF Funding details: Universiteit Stellenbosch, US, P26640-N25 P26132-N25, BodyRef/PDF/11228_2019_Article_523.pdf Funding details: Grantová Agentura
- Publisher
- Springer
- Relation
- Set-Valued and Variational Analysis Vol. 28, no. 3 (2020), p. 451-473, http://purl.org/au-research/grants/arc/DP160100854
- Rights
- Copyright © Springer Nature B.V. 2020
- Rights
- This metadata is freely available under a CCO license
- Rights
- Open Access
- Subject
- 0101 Pure Mathematics; Constraint system; Generalized differentiation; Metric subregularity; Radius theorems; Well-posedness
- Full Text
- Reviewed
- Funder
- Funding details: Austrian Science Fund, FWF, P26132-N25, P26640-N25, P29190-N32 Funding details: National Science Foundation, NSF Funding details: Australian Research Council, ARC Funding details: Australian Research Council, ARC, DP160100854 Funding details: Austrian Science Fund, FWF Funding details: Universiteit Stellenbosch, US, P26640-N25 P26132-N25, BodyRef/PDF/11228_2019_Article_523.pdf Funding details: Grantová Agentura
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