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<p>We propose a theoretical framework for solving split monotone variational inclusion problems involving maximally monotone operators in Hilbert spaces. Within this framework, we employ relaxed-inertial, self adaptive, and Tikhonov regularization techniques to develop an iterative algorithm for determining solutions to split monotone variational inclusion problems under appropriate hypotheses. Both theoretical analysis and numerical experiments along with real-world applications demonstrate the effectiveness of the proposed algorithm. We emphasize the main benefits of novel iterative approach compared to the classical algorithm for solving split monotone variational inclusion problems.</p>

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Solving split monotone variational inclusion problems via a relaxed-inertial self-adaptive regularized splitting algorithm

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Yasir Arfat,
  • Sorin-Mihai Grad,
  • Christiane Tammer,
  • Poom Kumam,
  • Muhammad Aqeel Ahmad Khan

摘要

We propose a theoretical framework for solving split monotone variational inclusion problems involving maximally monotone operators in Hilbert spaces. Within this framework, we employ relaxed-inertial, self adaptive, and Tikhonov regularization techniques to develop an iterative algorithm for determining solutions to split monotone variational inclusion problems under appropriate hypotheses. Both theoretical analysis and numerical experiments along with real-world applications demonstrate the effectiveness of the proposed algorithm. We emphasize the main benefits of novel iterative approach compared to the classical algorithm for solving split monotone variational inclusion problems.