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<p>The aim of this manuscript is to introduce a new self-adaptive algorithm designed to tackle the variational inequality problem over the solution set of the multiple-sets split feasibility problem with multiple output sets in Hilbert spaces. Our algorithm showcases strong convergence properties, eliminating the necessity for prior knowledge of Lipschitz and strongly monotone constants associated with the mapping. Moreover, it utilizes information from previous steps to guide its implementation, thus eliminating the necessity to compute or estimate the norm of the given operator. The paper presents various corollaries stemming from our main result. Finally, we present several numerical examples that illustrate the performance of our proposed algorithms in comparison to related algorithms.</p>

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A Novel Algorithm for Solving the Multiple-Sets Split Feasibility Problem with Multiple Output Sets

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • My Van Huynh Le,
  • Anh Viet Tran

摘要

The aim of this manuscript is to introduce a new self-adaptive algorithm designed to tackle the variational inequality problem over the solution set of the multiple-sets split feasibility problem with multiple output sets in Hilbert spaces. Our algorithm showcases strong convergence properties, eliminating the necessity for prior knowledge of Lipschitz and strongly monotone constants associated with the mapping. Moreover, it utilizes information from previous steps to guide its implementation, thus eliminating the necessity to compute or estimate the norm of the given operator. The paper presents various corollaries stemming from our main result. Finally, we present several numerical examples that illustrate the performance of our proposed algorithms in comparison to related algorithms.