Set regularities and feasibility problems

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between...

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Bibliographic Details
Published inMathematical programming Vol. 168; no. 1-2; pp. 279 - 311
Main Authors Kruger, Alexander Y., Luke, D. Russell, Thao, Nguyen H.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018
Springer Nature B.V
Subjects
Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Convergence
Euclidean space
Feasibility
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Projectors
Theoretical
65K05
Normal cone
Clarke regularity
Transversality
Normal qualification condition
Prox-regularity
Alternating projections
Secondary 49K40
CHIP
90C30
Douglas–Rachford
Hölder regularity
Weak-sharp minima
65K10
49M05
Metric regularity
49M37
Primary 49J53
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ISSN0025-5610
1436-4646
DOI10.1007/s10107-016-1039-x

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Summary:We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-1039-x