The operator extrapolation method for variational inequalities and its application

The study focuses on new iterative algorithms for solving monotone variational inequalities in Hilbert space. A variant of the operator extrapolation algorithm with a variable metric is proposed. Theorems on weak and strong convergence for variational inequalities with Lipschitz continuous and monotone operators are proved. Several applications of the operator extrapolation algorithm for saddle-type problems are considered. Keywords: variational inequality, saddle point problem, Nash equilibrium, operator equation, operator extrapolation method, variable metric method, convergence.