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<p>A backward inertial modification of the Bregman golden ratio algorithm is proposed for solving variational inequalities. The algorithm incorporates an inertial step, a Bregman distance, and a fully adaptive stepsize strategy. The convergence of the method is established under standard monotonicity and locally Lipschitz continuity assumptions, and a sublinear convergence rate is derived. Comparative numerical experiments illustrate the efficacy and applicability of the proposed approach, highlighting its advantages over existing techniques.</p>

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Backward Inertial Modification of the Bregman Golden Ratio Algorithm for Solving Variational Inequalities

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Grace Nnennaya Ogwo,
  • Chinedu Izuchukwu,
  • Yekini Shehu,
  • Xiaopeng Zhao

摘要

A backward inertial modification of the Bregman golden ratio algorithm is proposed for solving variational inequalities. The algorithm incorporates an inertial step, a Bregman distance, and a fully adaptive stepsize strategy. The convergence of the method is established under standard monotonicity and locally Lipschitz continuity assumptions, and a sublinear convergence rate is derived. Comparative numerical experiments illustrate the efficacy and applicability of the proposed approach, highlighting its advantages over existing techniques.