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Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications
Journal of Scientific Computing ( IF 2.5 ) Pub Date : 2021-03-02 , DOI: 10.1007/s10915-021-01428-9
Bing Tan , Xiaolong Qin , Jen-Chih Yao

In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.



中文翻译:

求解变分包含问题的自适应惯性算法的强收敛性及应用

本文介绍了四种具有惯性效应的自适应迭代算法,以解决实际希尔伯特空间中的分裂变分包含问题。所建议算法的优点之一是它们可以在不了解操作员规范的先验信息的情况下工作。这些算法的强收敛定理是在温和的和标准的假设下建立的。作为应用,研究了实际希尔伯特空间中的分裂可行性问题和分裂最小化问题。最后,提出了一些初步的数值实验以及压缩感测领域的实例,以支持所提出的方法相对于现有方法的优势和效率。

更新日期:2021-03-02
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