Convergence Analysis of a New Forward-Reflected-Backward Algorithm for Four Operators Without Cocoercivity

In this paper, we propose a new splitting algorithm to find the zero of a monotone inclusion problem that features the sum of three maximal monotone operators and a Lipschitz continuous monotone operator in Hilbert spaces. We prove that the sequence of iterates generated by our proposed splitting al...

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Vydáno v:Journal of optimization theory and applications Ročník 203; číslo 1; s. 256 - 284
Hlavní autoři: Cao, Yu, Wang, Yuanheng, ur Rehman, Habib, Shehu, Yekini, Yao, Jen-Chih
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.10.2024
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Engineering
Hilbert space
Iterative methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Splitting
Theory of Computation
Weak convergence
68Q25
Strong convergence
Maximal monotone
90C25
90C22
90C60
49M25
Lipschitz continuity
ISSN:0022-3239, 1573-2878
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Popis
Shrnutí:In this paper, we propose a new splitting algorithm to find the zero of a monotone inclusion problem that features the sum of three maximal monotone operators and a Lipschitz continuous monotone operator in Hilbert spaces. We prove that the sequence of iterates generated by our proposed splitting algorithm converges weakly to the zero of the considered inclusion problem under mild conditions on the iterative parameters. Several splitting algorithms in the literature are recovered as special cases of our proposed algorithm. Another interesting feature of our algorithm is that one forward evaluation of the Lipschitz continuous monotone operator is utilized at each iteration. Numerical results are given to support the theoretical analysis.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02501-7