MiKM: multi-step inertial Krasnosel’skiǐ–Mann algorithm and its applications

Q. L. Dong (), J. Z. Huang (), X. H. Li (), Y. J. Cho () and Th. M. Rassias ()
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Q. L. Dong: Civil Aviation University of China
J. Z. Huang: Chinese Academy of Sciences
X. H. Li: Civil Aviation University of China
Y. J. Cho: Gyeongsang National University
Th. M. Rassias: National Technical University of Athens

Journal of Global Optimization, 2019, vol. 73, issue 4, No 6, 824 pages

Abstract: Abstract 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.

Keywords: Nonexpansive operator; Multi-step inertial Krasnosel’skiǐ–Mann algorithm; Monotone inclusion; Bounded perturbation resilience; Douglas–Rachford splitting method; Forward–backward splitting method; Backward–forward splitting method; Davis–Yin splitting method (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-018-0727-x

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