Compositions and convex combinations of averaged nonexpansive operators

Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward–backward splitting algorithm for finding a zero of the sum of two monotone operators is...

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Veröffentlicht in:Journal of mathematical analysis and applications Jg. 425; H. 1; S. 55 - 70
Hauptverfasser: Combettes, Patrick L., Yamada, Isao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.05.2015
Elsevier
Schlagworte:
Averaged operator
Fixed-point algorithm
Forward–backward splitting
Mathematics
Monotone operator
Nonexpansive operator
Optimization and Control
Averaged operator
Nonexpansive operator
Monotone operator
Fixed-point algorithm
Forward–backward splitting
ISSN:0022-247X, 1096-0813
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Beschreibung
Zusammenfassung:Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward–backward splitting algorithm for finding a zero of the sum of two monotone operators is obtained.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.11.044