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<p>We propose a proximal-based iterative algorithm for a class of mixed set-valued quasi-variational inequality problems in Hilbert spaces, addressing both monotone and non-monotone cases. The method simply involves only one proximal operator and one cost operator evaluation per iteration, and uses adaptive step sizes together with a relaxed two-step inertial term. Convergence is established in the general setting and several special cases, with the non-monotone case handled under a novel assumption. Numerical experiments, including a generalized Nash-Cournot model, confirm the efficiency of the proposed approach compared with existing methods.</p>

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A Novel Proximal-Based Algorithm for Mixed Set-Valued Quasi-Variational Inequalities

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Xuan Thanh Le,
  • Tran Van Thang

摘要

We propose a proximal-based iterative algorithm for a class of mixed set-valued quasi-variational inequality problems in Hilbert spaces, addressing both monotone and non-monotone cases. The method simply involves only one proximal operator and one cost operator evaluation per iteration, and uses adaptive step sizes together with a relaxed two-step inertial term. Convergence is established in the general setting and several special cases, with the non-monotone case handled under a novel assumption. Numerical experiments, including a generalized Nash-Cournot model, confirm the efficiency of the proposed approach compared with existing methods.