Two-step Inertial Self-Adaptive Gradient Methods for the Split Feasibility Problem with Application
DOI:
https://doi.org/10.56919/usci.2652.013Keywords:
Fixed Point Problem, Iterative algorithm, Nonlinear Mappings, Weak and Strong ConvergentAbstract
This paper introduces novel two-step inertial self-adaptive gradient algorithms (TISGA) for solving the Split Feasibility Problem (SFP) in Hilbert spaces. The proposed method integrates dual inertial parameters and satisfying , together with a self-adaptive step-size where and is chosen to satisfy specific bounding conditions. This approach eliminates the requirement for prior knowledge of the bounded linear operator’s norm—a value often challenging to determine in practice. Under mild assumptions on the underlying operators, we establish weak convergence of the algorithm to a solution of the SFP. Numerical examples and an application are given to justify the theoretical results presented. The self-adaptive mechanism ensures practical implementability without norm estimation, while the two-step inertial acceleration potentially enhances convergence speed. This work extends and generalizes several established results in the existing literature, including one-step inertial methods and Euclidean-space two-step methods.
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