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<p>The purpose of this work is to propose some new conditions on the strong convergence for modified extragradient methods to find minimum-norm solutions of the variational inequality problem. We introduce two kinds of self-adaptive modified subgradient extragradient methods for solving variational inequality problems without any monotonicity of the cost mapping in a real Hilbert space. Finally, we give some numerical examples to illustrate the superiority of our proposed algorithms over the existing ones in the literature.</p>

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Some conditions for approximating solutions to non-monotone variational inequality problems

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Duong Viet Thong,
  • Abubakar Adamu,
  • Pham Thi Huong Huyen

摘要

The purpose of this work is to propose some new conditions on the strong convergence for modified extragradient methods to find minimum-norm solutions of the variational inequality problem. We introduce two kinds of self-adaptive modified subgradient extragradient methods for solving variational inequality problems without any monotonicity of the cost mapping in a real Hilbert space. Finally, we give some numerical examples to illustrate the superiority of our proposed algorithms over the existing ones in the literature.