• Ya. I. Vedel Faculty of Computer Science and Cybernetics, Taras Shevchenko Kiev National University, Kiev, Ukraine
  • V. V. Semenov Faculty of Computer Science and Cybernetics, Taras Shevchenko Kiev National University, Kiev, Ukraine
  • L. M. Chabak Faculty of Management and Technology, Infrastructure and Technology State University, Kiev, Ukraine
Keywords: equilibrium problem, two-stage proximal method, bifunction, pseudo-monotonicity, Lipschitz condition, Hilbert space, weak convergence


In this paper, the weak convergence of an iterative twostage proximal method for the approximate solution of the equilibrium problem in a Hilbert space is investigated. This method was recently been developed by Vedel and Semenov and can be used to solve mathematical programming problems, variational inequalities and game theory problems. The analysis of the convergence of the method was carried out under the assumption of the existence of a solution of the equilibrium problem and under conditions weaker than the previously considered ones.


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