• S. V. Denisov Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • V. V. Semenov Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • O. S. Kharkov Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Keywords: variational inequality, monotone operator, Alber generalized projection, 2-uniformly convex Banach space, uniformly smooth Banach space, algorithm, weak convergence, gap function


This work is devoted to the study of new iterative algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflectedbackward algorithm, which uses the Alber generalized projection instead of the metric one. The second algorithm is an adaptive version of the first one, where the monotone step size update rule is used, which does not require knowledge of Lipschitz constants and linear search procedure.


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