Asymptotic behavior of compositions of under-relaxed nonexpansive operators

Autor: Roberto Cominetti, Patrick L. Combettes, Jean-Bernard Baillon
Přispěvatelé: Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM), Université Paris 1 Panthéon-Sorbonne (UP1), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Departamento de Ingenieria Industrial [Santiago] (DII), David, Christian, Université Pierre et Marie Curie - Paris 6 (UPMC), Combettes, Patrick Louis
Jazyk: angličtina
Rok vydání: 2013
Předmět:
Statistics and Probability
Pure mathematics
0211 other engineering and technologies
02 engineering and technology
[MATH] Mathematics [math]
Fixed point
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
01 natural sciences
Cyclic projections
symbols.namesake
0101 mathematics
[MATH]Mathematics [math]
projection operator
Mathematics
Discrete mathematics
021103 operations research
Conjecture
2010 Mathematics Subject Classification. 47H09
47H10
47N10
65K15
Applied Mathematics
010102 general mathematics
[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]
Regular polygon
Hilbert space
[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]
Operator theory
Composition (combinatorics)
under-relaxed cycles
Linear subspace
fixed point
De Pierro's conjecture
Modeling and Simulation
symbols
Affine transformation
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
nonexpansive operator
Zdroj: Journal of Dynamics and Games (JDG)
Journal of Dynamics and Games (JDG), Springer, 2014, JDG, 1 (3), pp.331-346
Journal of Dynamics and Games
Journal of Dynamics and Games, 2014, 1 (3), pp.331-346. ⟨10.3934/jdg.2014.1.331⟩
Journal of Dynamics and Games, AIMS, 2014, 1, pp.331-346. ⟨10.3934/jdg.2014.1.331⟩
Journal of Dynamics and Games (JDG), 2014, JDG, 1 (3), pp.331-346
Journal of Dynamics and Games, 2014, 1, pp.331-346. ⟨10.3934/jdg.2014.1.331⟩
Journal of Dynamics and Games, AIMS, 2014, 1 (3), pp.331-346. ⟨10.3934/jdg.2014.1.331⟩
ISSN: 2164-6066
2164-6074
DOI: 10.3934/jdg.2014.1.331⟩
Popis: International audience; In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.
Databáze: OpenAIRE
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