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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Vydáno v:Acta mathematica vietnamica Ročník 49; číslo 2; s. 159 - 172
Hlavní autoři: Bằng, Vũ Công, Papadimitriou, Dimitri, Nhâm, Vũ Xuân
Médium: Journal Article
Jazyk:angličtina
Vydáno: Singapore Springer Nature Singapore 01.06.2024
Témata:
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
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Shrnutí: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