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This article aims to research iterative schemes for searching a solution of a quasimonotone variational inequality in a Hilbert space. For solving this quasimonotone variational inequality, we propose an iterative procedure which combines a self-adaptive rule and the extragradient algorithm. We demonstrate that the procedure weakly converges to the solution of the investigated quasimonotone variational inequality provided the considered operator satisfies several additional conditions.

A Self-Adaptive Extragradient Algorithm for Solving Quasimonotone Variational Inequalities