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<p>The study focuses on new iterative algorithms for solving monotone variational inequalities in a 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 to saddle-type problems are considered.</p>

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The Operator Extrapolation Method for Variational Inequalities and its Application

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • V. V. Semenov

摘要

The study focuses on new iterative algorithms for solving monotone variational inequalities in a 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 to saddle-type problems are considered.