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<p>In this paper, we introduce a new modified golden ratio algorithm with adaptive stepsize rules for solving non-monotone variational inequalities in infinite-dimensional Hilbert spaces. The weak convergence and convergence rate of the proposed algorithm are established under some standard conditions. Finally, to demonstrate the practical efficacy of our method, we give some numerical illustrations and we apply the proposed algorithm to solve a network equilibrium flow problem, which is a fundamental problem in transportation infrastructure modeling. Additionally, we compare the performance of our algorithm with other existing methods.</p>

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A Self Adaptive Projected Gradient Method for Solving Non-Monotone Variational Inequalities

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Duong Viet Thong,
  • Vu Tien Dung,
  • Hoang Thi Thanh Tam

摘要

In this paper, we introduce a new modified golden ratio algorithm with adaptive stepsize rules for solving non-monotone variational inequalities in infinite-dimensional Hilbert spaces. The weak convergence and convergence rate of the proposed algorithm are established under some standard conditions. Finally, to demonstrate the practical efficacy of our method, we give some numerical illustrations and we apply the proposed algorithm to solve a network equilibrium flow problem, which is a fundamental problem in transportation infrastructure modeling. Additionally, we compare the performance of our algorithm with other existing methods.