A generalized forward–backward splitting operator: degenerate analysis and applications

In this paper, we study the nonexpansive properties of a generalized forward–backward splitting (G-FBS) operator, particularly under the setting of degenerate metric, from which follow the convergence results in terms of degenerate metric of the associated fixed-point iterations. The descent lemma a...

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Veröffentlicht in:Computational & applied mathematics Jg. 42; H. 1
1. Verfasser: Xue, Feng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.02.2023
Schlagworte:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
68Q25
Degenerate metric
90C25
Generalized forward–backward splitting (G-FBS)
Operator splitting algorithms
47H09
47H05
Nonexpansive properties
ISSN:2238-3603, 1807-0302
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Zusammenfassung:In this paper, we study the nonexpansive properties of a generalized forward–backward splitting (G-FBS) operator, particularly under the setting of degenerate metric, from which follow the convergence results in terms of degenerate metric of the associated fixed-point iterations. The descent lemma and sufficient decrease property are also extended to degenerate case. It is further shown that the G-FBS operator provides a simplifying and unifying framework to model and analyze a great variety of operator splitting algorithms, and many existing results are exactly recovered or relaxed from our general results.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-022-02143-3