Chabak L. Projection algorithms for variational inequalities and equilibrium programming

The thesis is devoted to the development and theoretical substantiation of new effective algorithms for variational inequalities and equilibrium programming problems. Modifications of the subgradient extragradient algorithm, which does not require operators' lippsity, are constructed. New variants of regularization of weakly convergent algorithms for solving equilibrium problems in Hilbert space are developed. New algorithms for solving variational inequalities on a set of fixed points are proposed not more than the counted family of quasi-tensioning operators. Modifications of two-stage proximal algorithm using Bregman distance are constructed and theoretically grounded. To solve the variational inequalities with multivalued maximal monotone operators, a splitting algorithm has been developed and theoretically grounded.