About intrinsic transversality of pairs of sets

- Kruger, Alexander

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
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