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OPERATOR SPLITTING SCHEMES THROUGH A REGULARIZATION APPROACH

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Titel: OPERATOR SPLITTING SCHEMES THROUGH A REGULARIZATION APPROACH
Autoren: Moudafi, Abdellatif
Weitere Verfasser: MOUDAFI, Abdellatif
Verlagsinformationen: 2024.
Publikationsjahr: 2024
Schlagwörter: Forward-backward splitting algorithm, Halpern's iteration, Monotone operator, Sum, Krasnoselskii algorithm, [MATH] Mathematics [math], Resolvent, Reflected resolvent, Composition
Beschreibung: We propose a new algorithm for finding a zero of the sum of two monotone operators. It works by only requiring the evaluation of the resolvents of each of the operators individually, rather than the resolvent of their sum. We leverage then the connection with a co-coerciveness related operator, obtained by the sum and composition of Yosida regularization and reflected resolvents of the involved operators, to derive both a weak and a strong convergence results. The latter are provided by means of Krasnoselskii and Halpern celebrated classical Theorems.
Publikationsart: Article
Dateibeschreibung: application/pdf
Sprache: English
Zugangs-URL: https://amu.hal.science/hal-04211397v1
Dokumentencode: edsair.dedup.wf.002..5c99bc03f47c33883f3b8e4f111b2fa0
Datenbank: OpenAIRE
Beschreibung
Abstract:We propose a new algorithm for finding a zero of the sum of two monotone operators. It works by only requiring the evaluation of the resolvents of each of the operators individually, rather than the resolvent of their sum. We leverage then the connection with a co-coerciveness related operator, obtained by the sum and composition of Yosida regularization and reflected resolvents of the involved operators, to derive both a weak and a strong convergence results. The latter are provided by means of Krasnoselskii and Halpern celebrated classical Theorems.