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OPERATOR SPLITTING SCHEMES THROUGH A REGULARIZATION APPROACH

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Bibliographic Details
Title: OPERATOR SPLITTING SCHEMES THROUGH A REGULARIZATION APPROACH
Authors: Moudafi, Abdellatif
Contributors: MOUDAFI, Abdellatif
Publisher Information: 2024.
Publication Year: 2024
Subject Terms: Forward-backward splitting algorithm, Halpern's iteration, Monotone operator, Sum, Krasnoselskii algorithm, [MATH] Mathematics [math], Resolvent, Reflected resolvent, Composition
Description: 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.
Document Type: Article
File Description: application/pdf
Language: English
Access URL: https://amu.hal.science/hal-04211397v1
Accession Number: edsair.dedup.wf.002..5c99bc03f47c33883f3b8e4f111b2fa0
Database: OpenAIRE
Description
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.