A Primal-dual Backward Reflected Forward Splitting Algorithm for Structured Monotone Inclusions

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusions in real Hilbert spaces. The algorithm allows to use the inexact computations of Lipschitzian and cocoercive operators. The strong convergence of the generated iterative sequenc...

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Bibliographic Details
Published in:Acta mathematica vietnamica Vol. 49; no. 2; pp. 159 - 172
Main Authors: Bằng, Vũ Công, Papadimitriou, Dimitri, Nhâm, Vũ Xuân
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.06.2024
Subjects:
Mathematics
Mathematics and Statistics
Forward-backward
Cocoercive
Monotone inclusion
Primal-dual algorithm
Monotone operator
Duality
Lipschitz
Backward-forward
90C25
Operator splitting
Composite operator
49M29
49M27
47H05
ISSN:0251-4184, 2315-4144
Online Access:Get full text
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Summary:We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusions in real Hilbert spaces. The algorithm allows to use the inexact computations of Lipschitzian and cocoercive operators. The strong convergence of the generated iterative sequence is proved under the strong monotonicity condition, whilst the weak convergence is formally proved under several conditions used in the literature. An application to a structured minimization problem is provided.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-024-00535-7