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<p>This paper introduces a new algorithm for solving strongly monotone variational inequality problems over the solution set of the multiple-sets split variational inequality problem. We prove that the algorithm converges strongly without requiring knowledge of the Lipschitz or strongly monotone constants of the mappings. Moreover, no prior information about the norm of the bounded linear operator is necessary. Special cases are discussed, and numerical examples are presented to illustrate the performance of the algorithm.</p>

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A novel algorithm for strongly monotone variational inequalities with the multiple-sets split variational inequality problem constraints

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • Tran Viet Anh

摘要

This paper introduces a new algorithm for solving strongly monotone variational inequality problems over the solution set of the multiple-sets split variational inequality problem. We prove that the algorithm converges strongly without requiring knowledge of the Lipschitz or strongly monotone constants of the mappings. Moreover, no prior information about the norm of the bounded linear operator is necessary. Special cases are discussed, and numerical examples are presented to illustrate the performance of the algorithm.