An Inertial and Relaxed Projection Algorithm for the Split Feasibility Problem in Hilbert Spaces
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Tóm tắt
In this paper, we propose a new self-adaptive inertial and relaxed CQ algorithm for solving the split feasibility problem in real Hilbert spaces. The method incorporates alternated inertial extrapolation, a conjugate-gradient-inspired search direction, and a self-adaptive step-size strategy, which eliminates the need for operator norm evaluations or line search procedures. Under suitable assumptions, we establish strong convergence of the generated sequence to the minimum-norm solution of the problem. To illustrate the practical applicability of the proposed method, we apply it to an elastic net regularization model. The numerical experiment shows that the algorithm converges effectively and is suitable for high-dimensional regression problems
Từ khóa
Split Feasibility Problem, Hilbert Space, Inertial Method, Conjugate Gradient-Type Direction, Adaptive Step Size, Strong Convergence
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Tài liệu tham khảo
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