Two self-adaptive inertial projection algorithms for solving split variational inclusion problems

Zheng Zhou; Bing Tan; Songxiao Li; Zheng Zhou; Bing Tan; Songxiao Li

doi:10.3934/math.2022276

AIMS Mathematics

2022, Volume 7, Issue 4: 4960-4973. doi: 10.3934/math.2022276

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Research article

Two self-adaptive inertial projection algorithms for solving split variational inclusion problems

Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Received: 17 June 2021 Revised: 22 December 2021 Accepted: 23 December 2021 Published: 29 December 2021
MSC : 47H05, 49J40, 65K10, 65Y10

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.
- self-adaptive stepsize,
- projection algorithm,
- inertial technique,
- split variational inclusion problem
Citation: Zheng Zhou, Bing Tan, Songxiao Li. Two self-adaptive inertial projection algorithms for solving split variational inclusion problems[J]. AIMS Mathematics, 2022, 7(4): 4960-4973. doi: 10.3934/math.2022276

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Abstract

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.

References

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