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<p>In this paper, we introduce two self-adaptive subgradient extragradient methods for solving non-monotone variational inequalities involving non-Lipschitz mappings in real Hilbert space. Under weaker conditions than the existing conditions, we investigate and present strong convergence theorems of the proposed algorithms. Our results extend and improve the studied results in the literature. Finally, we give an application to image restoration and some numerical experiments to demonstrate the efficiency of our proposed algorithms.</p>

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Solving Non-monotone Variational Inequality Problems Involving Non-Lipschitz Mappings with Application to Image Restoration

  • 期刊论文

  • 发表日期：

    2026年4月25日

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  • Abubakar Adamu,
  • Duong Viet Thong,
  • Nguyen Thi An,
  • Dang Huy Ngan

摘要

In this paper, we introduce two self-adaptive subgradient extragradient methods for solving non-monotone variational inequalities involving non-Lipschitz mappings in real Hilbert space. Under weaker conditions than the existing conditions, we investigate and present strong convergence theorems of the proposed algorithms. Our results extend and improve the studied results in the literature. Finally, we give an application to image restoration and some numerical experiments to demonstrate the efficiency of our proposed algorithms.