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<p>This paper introduces a novel algorithm for solving strongly monotone variational inequality problems with the split variational inequality problem with multiple output sets constraints. Within the context of real Hilbert spaces, our method incorporates self-adaptive step sizes derived from preceding step data, enabling implementation without prior knowledge of bounded linear operators’ norms. Remarkably, our algorithm operates effectively without explicit knowledge of Lipschitz and strongly monotone constants of the mappings. Finally, we offer several numerical examples to illustrate the performance of our proposed algorithm.</p>

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A Novel Algorithm with Self-Adaptive Technique for Variational Inequalities with the Split Variational Inequality Problem with Multiple Output Sets Constraints

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Le Huynh My Van,
  • Tran Viet Anh,
  • Nguyen Dinh Huy

摘要

This paper introduces a novel algorithm for solving strongly monotone variational inequality problems with the split variational inequality problem with multiple output sets constraints. Within the context of real Hilbert spaces, our method incorporates self-adaptive step sizes derived from preceding step data, enabling implementation without prior knowledge of bounded linear operators’ norms. Remarkably, our algorithm operates effectively without explicit knowledge of Lipschitz and strongly monotone constants of the mappings. Finally, we offer several numerical examples to illustrate the performance of our proposed algorithm.