非扩张映射的广义修正两步惯性Mann Halpern算法
Generalized Modified Two-Step Inertial Mann Halpern Algorithm for Nonexpansive Mappings
DOI: 10.12677/aam.2025.148380, PDF,   
作者: 李钱涛：福州大学数学与统计学院，福建 福州
关键词: 两步惯性；Mann算法；非扩张映射；强收敛性；Two-Step Inertial； Mann Algorithm； Nonexpansive Mapping； Strong Convergence
摘要: 受广义Krasnoselskii-Mann算法和两步惯性项应用的启发，本文提出了一种求解非扩张映射不动点问题的广义修正两步惯性Mann Halpern算法。在一定合适的条件下，本文证明了算法的强收敛性。在数值实验中，本文将算法用于解决凸可行问题。数值结果表明，在某些情况下，该算法更具优势。
Abstract: Motivated by the application generalized Krasnoselskii-Mann algorithm and two-step inertial extrapolation, this paper proposes a generalized modified two-step inertial Mann Halpern algorithm for solving fixed point problems with nonexpansive mapping. Under mild assumptions, the strong convergence of the proposed method are established. In numerical experiment, a convex feasibility problem is solved. Numerical results demonstrate that our algorithm has advantages in some cases.
文章引用：李钱涛. 非扩张映射的广义修正两步惯性Mann Halpern算法[J]. 应用数学进展, 2025, 14(8): 160-169. https://doi.org/10.12677/aam.2025.148380

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