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<p>In this paper, we address a general bilevel variational inequality problem that incorporates variational inequalities defined over the intersection of the common fixed points of a finite family of generalized demimetric mappings and the solutions to a quasi-monotone variational inequality. We introduce a novel projection contraction-type algorithm that employs an inertial approach with three correction terms to accelerate convergence. We establish the strong convergence of the proposed algorithm under appropriate conditions on the parameters. Additionally, we provide numerical examples to illustrate and assess the effectiveness of our method.</p>

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A new accelerated projection contraction algorithm for solving bilevel variational inequalities involving quasi-monotone variational inequalities and fixed point problems

  • 期刊论文

  • 发表日期：

    2025年10月30日

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  • Mohammad Eslamian,
  • Ahmad Kamandi

摘要

In this paper, we address a general bilevel variational inequality problem that incorporates variational inequalities defined over the intersection of the common fixed points of a finite family of generalized demimetric mappings and the solutions to a quasi-monotone variational inequality. We introduce a novel projection contraction-type algorithm that employs an inertial approach with three correction terms to accelerate convergence. We establish the strong convergence of the proposed algorithm under appropriate conditions on the parameters. Additionally, we provide numerical examples to illustrate and assess the effectiveness of our method.