Scholarlink

<p>This paper proposes a Double Inertial Golden Ratio Method (DI-GRM) for solving non-Lipschitz pseudomonotone variational inequality problems (VIPs) in Hilbert spaces. The algorithm integrates subgradient and extragradient steps with Armijo-type line search and Mann iteration. The inertial component accelerates convergence by leveraging momentum, while the golden ratio mechanism stabilizes extrapolation. We prove weak convergence under general pseudomonotonicity and establish <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( R \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>R</mi> </math></EquationSource> </InlineEquation>-linear convergence under strong pseudomonotonicity. Numerical experiments demonstrate the method’s superior performance compared to existing algorithms across diverse VIP instances.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Golden Ratio Algorithm with Inertia for Non-Lipschitz Variational Inequalities

  • 期刊论文

  • 发表日期：

    2026年3月26日

查看全文
  • Vahid Darvish,
  • Godwin Chidi Ugwunnadi,
  • Aniefiok Udomene,
  • Habib ur Rehman

摘要

This paper proposes a Double Inertial Golden Ratio Method (DI-GRM) for solving non-Lipschitz pseudomonotone variational inequality problems (VIPs) in Hilbert spaces. The algorithm integrates subgradient and extragradient steps with Armijo-type line search and Mann iteration. The inertial component accelerates convergence by leveraging momentum, while the golden ratio mechanism stabilizes extrapolation. We prove weak convergence under general pseudomonotonicity and establish \( R \) R -linear convergence under strong pseudomonotonicity. Numerical experiments demonstrate the method’s superior performance compared to existing algorithms across diverse VIP instances.