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<p>In this paper, we present and study two strongly convergent two-step inertial accelerated algorithms for solving pseudo-monotone variational inequality problem. Our methods are modification and extension of the Halpern-type method previously studied in the literature. Unique feature of our methods is their ability to handle non-Lipschitz continuous and pseudo-monotone operator through a novel line-search rule. Additionally, the two-step inertial technique incorporated in our methods account for the improvement in the rate of convergence. Finally, we compare our methods with some well-known methods in the literature through numerical experiments. The numerical results reveal that the proposed methods perform better than these methods.</p>

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Strong convergence results of two-step inertial projection algorithms for solving variational inequality problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月19日

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  • Kalu Okam Okorie,
  • Chibueze Christian Okeke,
  • Chinedu Izuchukwu,
  • Dilber Uzun Ozasahin,
  • Abubakar Adamu

摘要

In this paper, we present and study two strongly convergent two-step inertial accelerated algorithms for solving pseudo-monotone variational inequality problem. Our methods are modification and extension of the Halpern-type method previously studied in the literature. Unique feature of our methods is their ability to handle non-Lipschitz continuous and pseudo-monotone operator through a novel line-search rule. Additionally, the two-step inertial technique incorporated in our methods account for the improvement in the rate of convergence. Finally, we compare our methods with some well-known methods in the literature through numerical experiments. The numerical results reveal that the proposed methods perform better than these methods.