- Title
- About intrinsic transversality of pairs of sets
- Creator
- Kruger, Alexander
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/164744
- Identifier
- vital:13102
- Identifier
-
https://doi.org/10.1007/s11228-017-0446-3
- Identifier
- ISBN:0927-6947 (ISSN)
- Abstract
- The article continues the study of the ‘regular’ arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification conditions in optimization as well as subdifferential, normal cone and coderivative calculus, and convergence analysis of computational algorithms. One of the main motivations for the development of the transversality theory of collections of sets comes from the convergence analysis of alternating projections for solving feasibility problems. This article targets infinite dimensional extensions of the intrinsic transversality property introduced recently by Drusvyatskiy, Ioffe and Lewis as a sufficient condition for local linear convergence of alternating projections. Several characterizations of this property are established involving new limiting objects defined for pairs of sets. Special attention is given to the convex case.
- Publisher
- Springer Netherlands
- Relation
- Set-Valued and Variational Analysis Vol. 26, no. 1 (2018), p. 111-142; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- Copyright © 2017, Springer Science+Business Media B.V.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; Alternating projections; Intrinsic transversality; Linear convergence; Metric regularity; Metric subregularity; Normal cone; Subtransversality; Transversality
- Full Text
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