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A Gradient-Like Regularized Dynamics for Monotone Equilibrium Problems

  • Pham Ky Anh [2] ; Trinh Ngoc Hai [1] ; Vu Tien Dung [2]
    1. [1] Hanoi University of Science and Technology

      Hanoi University of Science and Technology

      Vietnam

    2. [2] Vietnam National University
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this paper, a gradient-like regularized dynamical system associated with a mono-tone equilibrium problem is studied. First, we give a rigorous proof of the existenceand uniqueness of the strong global solution to the dynamical system. Then, we obtainstrong convergence of the generated trajectories to a solution of the original equilib-rium. A time discretization of the dynamical system provides a strongly convergentiterative regularization gradient-type method with relaxation parameters. Finally, theperformance of the regularized dynamical system approach is illustrated by numericalexperiments.

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