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A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces

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Abstract

In this paper, we propose a new algorithm with inertial term and self-adaptive stepsize for solving the split variational inclusion problem (denoted by SVIP) in real Hilbert spaces. Under suitable conditions imposed on the parameters, we prove that our iterative scheme converges strongly to an element of the solution set of SVIP without the prior knowledge of the operator norm. Furthermore, we demonstrate that our suggested algorithm is efficient and achievable through some numerical experiments.

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Funding

This work was supported by the Natural Science Foundation of China (Grant No. 12171062) and the Natural Science Foundation of Chongqing (Grant No. CSTB2022NSCQ-JQX0004), Chongqing’s youth talent support program (Grant No. cstc2021ycjh-bgzxm0130).

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Pingjing Xia & Gang Cai

  2. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong

Authors
  1. Pingjing Xia
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  2. Gang Cai
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  3. Qiao-Li Dong
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Contributions

Xia and Cai wrote the main manuscript text and Dong finished the numerical examples. All authors reviewed the manuscript.

Corresponding author

Correspondence to Gang Cai.

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Xia, P., Cai, G. & Dong, QL. A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces. Netw Spat Econ 23, 931–952 (2023). https://doi.org/10.1007/s11067-023-09600-4

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