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Two Optimization Approaches for Solving Split Variational Inclusion Problems with Applications

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Abstract

Using inertial effects, novel defined parameters and proximal-like algorithms with new variable stepsize rules, we propose two efficient optimization approaches for solving split variational inclusion problems in Hilbert spaces. Contrary with the work by Tang and Gibali (Numer Algorithms 83:305–331, 2020) and by Tan et al. (J Sci Comput 87:20, 2021), the proposed approaches do not require their stepsizes tending to zero and computing six values of the cost functions per iteration. These features can accelerate our methods. Weak and strong convergence of the introduced approaches are established without Lipschitz continuity of the cost functions and firm-nonexpansiveness of the proximal mappings. As applications, we mainly focus on the split feasibility and split minimization problems. Finally, several numerical experiments are provided for illustration and comparison.

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Funding

The second author was supported by National Natural Science Foundation of China (Grant No. 11801430).

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  1. Xidian University School of Mathematics and Statistics, Xi’an, 710126, Shaanxi, China

    Xiaojun Ma, Hongwei Liu & Xiaoyin Li

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  1. Xiaojun Ma
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  2. Hongwei Liu
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Correspondence to Xiaojun Ma.

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Ma, X., Liu, H. & Li, X. Two Optimization Approaches for Solving Split Variational Inclusion Problems with Applications. J Sci Comput 91, 58 (2022). https://doi.org/10.1007/s10915-022-01832-9

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