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<p>In this paper, we design proximal-type algorithms with reflections to solve variational inequalities. The proposed algorithms are studied for constant and self-adaptive non-decreasing step sizes. In each case, we obtain weak and strong convergence results. Both algorithms feature one forward evaluation and one proximal evaluation at each iteration. We give numerical examples to show that our algorithms outperform related ones in the literature.</p>

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Convergence results of proximal-type algorithms with reflections for variational inequalities

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Yonghong Yao,
  • Sani Salisu,
  • Yekini Shehu

摘要

In this paper, we design proximal-type algorithms with reflections to solve variational inequalities. The proposed algorithms are studied for constant and self-adaptive non-decreasing step sizes. In each case, we obtain weak and strong convergence results. Both algorithms feature one forward evaluation and one proximal evaluation at each iteration. We give numerical examples to show that our algorithms outperform related ones in the literature.