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<p>In this paper, we put forward a modified extragradient method with Bregman divergence and a novel stepsize rule for solving pseudo-monotone variational inequality problems in reflexive Banach spaces, this new stepsize is the combination of self-adjustment stepsize and line-search stepsize. Under some suitable constraints imposed on the operators and parameters, we establish a strong convergence theorem for the proposed algorithm. In addition, we give two new algorithms in a real Hilbert space: a Tseng-type method and a subgradient extragradient method, and prove their weak convergence and R-linear convergence results. Moreover, our algorithms do not require prior knowledge of Lipschitz constant for the operators. Finally, some numerical experiments are given to illustrate the performance of our proposed algorithms.</p>

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Convergence Analysis of Modified Bregman Extragradient Method for Variational Inequality Problems

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Qingqing Fu,
  • Gang Cai,
  • Kunrada Kankam,
  • Prasit Cholamjiak

摘要

In this paper, we put forward a modified extragradient method with Bregman divergence and a novel stepsize rule for solving pseudo-monotone variational inequality problems in reflexive Banach spaces, this new stepsize is the combination of self-adjustment stepsize and line-search stepsize. Under some suitable constraints imposed on the operators and parameters, we establish a strong convergence theorem for the proposed algorithm. In addition, we give two new algorithms in a real Hilbert space: a Tseng-type method and a subgradient extragradient method, and prove their weak convergence and R-linear convergence results. Moreover, our algorithms do not require prior knowledge of Lipschitz constant for the operators. Finally, some numerical experiments are given to illustrate the performance of our proposed algorithms.