New methods improve convergence of saddle point problems in Hilbert space, suggesting enhanced solutions.
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.
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V. V. Semenov (2025) studied this question.
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