In this paper, we first study a relaxed inertial projection and contraction method for variational inequalities to obtain weak convergence results under standard assumptions in Hilbert spaces. Next, we propose another inertial projection and contraction method for which the inertial factor θ is chosen in $[0,1]$ with $\theta =1$ possible. Weak and linear convergence are obtained for this second proposed method. As far as we know, the choice $\theta =1$ has not been considered before in the literature for inertial projection and contraction method. Finally, we give some numerical illustrations of our methods.

中文翻译：

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松弛惯性投影与收缩方法的版本分析

在本文中，我们首先研究了变分不等式的松弛惯性投影和收缩方法，以获得标准假设下希尔伯特空间中的弱收敛结果。接下来，我们提出另一种惯性投影和收缩方法，为此选择惯性因子θ$[0，\mathrm{1个}]$ 和 $\theta =\mathrm{1个}$可能的。此第二种建议方法获得了弱收敛和线性收敛。据我们所知，选择$\theta =\mathrm{1个}$惯性投影和收缩方法尚未在文献中考虑过。最后，我们对方法进行了一些数值说明。