About Intrinsic Transversality of Pairs of Sets

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...

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Vydáno v:Set-valued and variational analysis Ročník 26; číslo 1; s. 111 - 142
Hlavní autor: Kruger, Alexander Y.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.03.2018
Springer Nature B.V
Témata:
Analysis
Calculus
Convergence
Feasibility studies
Mathematics
Mathematics and Statistics
Optimization
Metric subregularity
65K05
Normal cone
Transversality
Alternating projections
Linear convergence
Secondary 49K40
90C30
Intrinsic transversality
65K10
49M05
Metric regularity
49M37
Primary 49J53
Subtransversality
ISSN:1877-0533, 1877-0541
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-017-0446-3