In this paper, we present and study two new two-step inertial accelerated algorithms for finding an approximate solution of split feasibility problems with multiple output sets. Our methods are extensions of CQ algorithms previously studied in the literature. In contrast to the related iterative methods for solving SFP, our methods incorporate a two-step inertial technique that speeds up the convergence rate of the generated sequences to the unique solution of SFP studied in this work. Furthermore, we present weak and strong convergence results where the strong convergence result of our method is obtained without the on-line rule, a feature absent in related algorithms in the literature. Finally, we demonstrate the applicability and performance of our algorithms through numerical experiments. Our numerical results reveal that our methods perform better than existing related methods in the literature.

中文翻译：

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用于求解具有多个输出集的分裂可行性问题的两步惯性加速算法


在本文中，我们提出并研究了两种新的两步惯性加速算法，用于寻找具有多个输出集的分裂可行性问题的近似解。我们的方法是先前在文献中研究的 CQ 算法的扩展。与求解 SFP 的相关迭代方法相比，我们的方法采用了两步惯性技术，该技术加快了生成序列的收敛速度，以达到本研究中研究的 SFP 的独特解。此外，我们提出了弱收敛和强收敛结果，其中我们方法的强收敛结果是在没有在线规则的情况下获得的，这是文献中相关算法中不存在的特征。最后，我们通过数值实验证明了算法的适用性和性能。我们的数值结果表明，我们的方法比文献中现有的相关方法性能更好。