Set regularities and feasibility problems

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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Veröffentlicht in:Mathematical programming 2018-03, Vol.168 (1-2), p.279-311
Hauptverfasser: Kruger, Alexander Y., Luke, D. Russell, Thao, Nguyen H.
Format: Artikel
Sprache:eng
Schlagworte:
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
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Beschreibung
Zusammenfassung: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.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-1039-x