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Chang, Shih-sen; Yao, Jen-Chih; Wang, Lin; Liu, Min; Zhao, Liangcai

On the inertial forward-backward splitting technique for solving a system of inclusion problems in Hilbert spaces. (English) Zbl 07442336

Optimization 70, No. 12, 2511-2525 (2021).
Summary: The purpose of this paper is to introduce and study the existence problem of solution for a system of monotone variational inclusion problems in Hilbert spaces. By using the inertial forward-backward splitting technique, we propose and analyze an algorithm. Under suitable conditions, we proved that the sequence generated by the algorithm converges strongly to a solution of such kind of monotone variational inclusion problems. At the end of the paper, some applications are also given. The results presented in the paper extend and improve some recent results.

Cited in 9 Documents

MSC:

47-XX Operator theory
26A18 Iteration of real functions in one variable
47H04 Set-valued operators
47H05 Monotone operators and generalizations
47H10 Fixed-point theorems

Keywords:

inertial forward-backward splitting technique; maximal monotone operators; inverse strongly monotone operator; monotone inclusion; averaged operator
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References:

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