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<p>In this paper, we propose an accelerated and relaxed algorithm for solving the Split Feasibility Problem with Multiple Output Sets (SFP-MOS) in real Hilbert spaces. The method features an alternated inertial extrapolation scheme embedded in a two-term conjugate-gradient-like direction, which improves stability and convergence efficiency. An adaptive step-size rule is employed, avoiding the need for operator norm evaluations or costly line searches. We prove strong convergence of the generated sequence to the minimum-norm solution under mild assumptions. The algorithm is applied to elastic net regularization and image classification tasks. Numerical experiments demonstrate its robustness, computational efficiency, and superior performance compared to several state-of-the-art methods in terms of generalization and runtime.</p>

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An accelerated relaxed algorithm for the split feasibility problem with multiple output sets in Hilbert spaces

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Nguyen Thi Thu Thuy,
  • Nguyen Quoc Anh

摘要

In this paper, we propose an accelerated and relaxed algorithm for solving the Split Feasibility Problem with Multiple Output Sets (SFP-MOS) in real Hilbert spaces. The method features an alternated inertial extrapolation scheme embedded in a two-term conjugate-gradient-like direction, which improves stability and convergence efficiency. An adaptive step-size rule is employed, avoiding the need for operator norm evaluations or costly line searches. We prove strong convergence of the generated sequence to the minimum-norm solution under mild assumptions. The algorithm is applied to elastic net regularization and image classification tasks. Numerical experiments demonstrate its robustness, computational efficiency, and superior performance compared to several state-of-the-art methods in terms of generalization and runtime.