A new modified Halpern-type splitting algorithm for solving monotone inclusion problems in reflexive Banach spaces

This paper mainly introduces a new modified Halpern-type splitting algorithm for solving the monotone inclusion problem in real reflexive Banach spaces. Furthermore, the strong convergence of the sequence generated by our algorithm is proved under some mild assumptions imposed on the operators and p...

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Published in:Journal of global optimization Vol. 91; no. 3; pp. 559 - 585
Main Authors: Chen, Lulu, Cai, Gang, Cholamjiak, Prasit, Inkrong, Papatsara
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2025
Springer Nature B.V
Subjects:
Algorithms
Banach spaces
Computer Science
Hilbert space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Splitting
Strong convergence
47H10
Maximal monotone operator
47H07
Banach spaces
Inclusion problem
47H05
54H25
ISSN:0925-5001, 1573-2916
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Abstract This paper mainly introduces a new modified Halpern-type splitting algorithm for solving the monotone inclusion problem in real reflexive Banach spaces. Furthermore, the strong convergence of the sequence generated by our algorithm is proved under some mild assumptions imposed on the operators and parameters. Finally, several numerical experiments are performed, which illustrate the effectiveness of our algorithm.
AbstractList This paper mainly introduces a new modified Halpern-type splitting algorithm for solving the monotone inclusion problem in real reflexive Banach spaces. Furthermore, the strong convergence of the sequence generated by our algorithm is proved under some mild assumptions imposed on the operators and parameters. Finally, several numerical experiments are performed, which illustrate the effectiveness of our algorithm.
Author Cai, Gang
Inkrong, Papatsara
Chen, Lulu
Cholamjiak, Prasit
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  fullname: Cholamjiak, Prasit
  organization: School of Science, University of Phayao
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  givenname: Papatsara
  surname: Inkrong
  fullname: Inkrong, Papatsara
  organization: School of Science, University of Phayao
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Maximal monotone operator
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Banach spaces
Inclusion problem
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Snippet This paper mainly introduces a new modified Halpern-type splitting algorithm for solving the monotone inclusion problem in real reflexive Banach spaces....
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SubjectTerms Algorithms
Banach spaces
Computer Science
Hilbert space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Splitting
Title A new modified Halpern-type splitting algorithm for solving monotone inclusion problems in reflexive Banach spaces
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