MiKM: multi-step inertial Krasnosel’skiǐ-Mann algorithm and its applications. In this paper, we first introduce a multi-step inertial Krasnosel’skiǐ-Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces. We give the convergence of the MiKM by investigating the convergence of the Krasnosel’skiǐ-Mann algorithm with perturbations. We also establish global pointwise and ergodic iteration complexity bounds of the Krasnosel’skiǐ-Mann algorithm with perturbations. Based on the MiKM, we construct some multi-step inertial splitting methods, including the multi-step inertial Douglas-Rachford splitting method (MiDRS), the multi-step inertial forward-backward splitting method, multi-step inertial backward-forward splitting method and and the multi-step inertial Davis-Yin splitting method. Numerical experiments are provided to illustrate the advantage of the MiDRS over the one-step inertial DRS and the original DRS.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Tang, Yan; Lin, Honghua; Gibali, Aviv; Cho, Yeol Je: Convergence analysis and applications of the inertial algorithm solving inclusion problems (2022)
  2. Alakoya, Timilehin Opeyemi; Taiwo, Adeolu; Mewomo, Oluwatosin Temitope; Cho, Yeol Je: An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings (2021)
  3. Attouch, Hedy: Fast inertial proximal ADMM algorithms for convex structured optimization with linear constraint (2021)
  4. Dong, Qiao-Li; He, Songnian; Liu, Lulu: A general inertial projected gradient method for variational inequality problems (2021)
  5. Dong, Qiao-Li; Li, Xiao-Huan; Cho, Yeol Je; Rassias, Themistocles M.: Multi-step inertial Krasnosel’skiǐ-Mann iteration with new inertial parameters arrays (2021)
  6. He, Songnian; Dong, Qiao-Li; Tian, Hanlin; Li, Xiao-Huan: On the optimal relaxation parameters of Krasnosel’skiǐ-Mann iteration (2021)
  7. Li, Haiying; Wu, Yulian; Wang, Fenghui: New inertial relaxed (CQ) algorithms for solving split feasibility problems in Hilbert spaces (2021)
  8. Rehman, Habib ur; Gibali, Aviv; Kumam, Poom; Sitthithakerngkiet, Kanokwan: Two new extragradient methods for solving equilibrium problems (2021)
  9. Sahu, D. R.; Cho, Y. J.; Dong, Q. L.; Kashyap, M. R.; Li, X. H.: Inertial relaxed \textitCQalgorithms for solving a split feasibility problem in Hilbert spaces (2021)
  10. Ur Rehman, Habib; Kumam, Poom; Gibali, Aviv; Kumam, Wiyada: Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications (2021)
  11. Hieu, Dang Van; Strodiot, Jean Jacques; Muu, Le Dung: An explicit extragradient algorithm for solving variational inequalities (2020)
  12. Dong, Q. L.; Huang, J. Z.; Li, X. H.; Cho, Y. J.; Rassias, Th. M.: MiKM: multi-step inertial Krasnosel’skiǐ-Mann algorithm and its applications (2019)
  13. Heaton, Howard; Censor, Yair: Asynchronous sequential inertial iterations for common fixed points problems with an application to linear systems (2019)