We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.

中文翻译：

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求解希尔伯特空间变分不等式的次梯度超梯度法

我们提出了一种用于解决希尔伯特空间中的变分不等式的次梯度超梯度方法。此外，我们提出了我们算法的修改版本，该版本可以找到变分不等式的解，该不等式也是给定非扩展映射的不动点。我们为这两种算法建立了弱收敛定理。