Semenov V.V., Denisov S.V., Sandrakov G.V., Kharkov O.S.
Convergence of extrapolation from the past method for variational inequalities in uniformly convex Banach spaces

New iterative algorithms for solving variational inequalities in uniformly convex Banach spaces are analyzed. The first algorithm is a modification of the forward-reflected-backward method, 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 the Lipschitz constants and linear search procedure. For variational inequalities with monotone Lipschitz operators acting in a 2-uniformly convex and uniformly smooth Banach space, theorems on the weak convergence of the methods are proved. Also, for the first algorithm, an efficiency estimate in terms of the gap function is proved. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: 2-uniformly convex Banach space, Alber generalized projection, gap function, monotone operator, operator extrapolation method, uniformly smooth Banach space, variational inequality, weak convergence, Extrapolation, Iterative methods, Variational techniques, 2-uniformly convex banach space, Alber generalized projection, Extrapolation methods, Gap functions, Generalized projections, Monotone operators, Operator extrapolation method, Uniformly convex Banach space, Uniformly smooth banach space, Variational inequalities, Weak convergence, Banach spaces

Cite:
Semenov V.V., Denisov S.V., Sandrakov G.V., Kharkov O.S. (2022). Convergence of extrapolation from the past method for variational inequalities in uniformly convex Banach spaces. Cybernetics and Systems Analysis, 58 (4), 82–93. doi: https://doi.org/10.1007/s10559-022-00507-5 http://jnas.nbuv.gov.ua/article/UJRN-0001335522 [In Ukrainian].