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<p>In this paper, an Armijo−Type viscosity algorithm is proposed to solve continuous equilibrium problems without monotonicity on Hadamard manifolds. The iterative sequence generated by the algorithm is shown to converge to a solution of these equilibrium problems on Hadamard manifold under some mild conditions. Meanwhile, the convergence rate of the algorithm is obtained. In addition, the results obtained in this paper is used to solve variational inequality problems and convex minimization problems, and two numerical experiments are provided to verify the effectiveness of the algorithm.</p>

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An Armijo−Type viscosity algorithm for continuous equilibrium problems without monotonicity on Hadamard manifolds

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Wanning Yang,
  • Lin Wang,
  • Zhaoli Ma,
  • Liang Yan

摘要

In this paper, an Armijo−Type viscosity algorithm is proposed to solve continuous equilibrium problems without monotonicity on Hadamard manifolds. The iterative sequence generated by the algorithm is shown to converge to a solution of these equilibrium problems on Hadamard manifold under some mild conditions. Meanwhile, the convergence rate of the algorithm is obtained. In addition, the results obtained in this paper is used to solve variational inequality problems and convex minimization problems, and two numerical experiments are provided to verify the effectiveness of the algorithm.