In this work, we propose a self-adaptive projection method for solving variational inequalities with Lipschitz continuous and quasimonotone mapping (or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Using the technique of double inertial steps into a single projection method, we give weak and strong convergence theorems of the proposed algorithm. The results obtained in this paper extend some recent results in the literature.

中文翻译：

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一种求解拟单调变分不等式的改进的非单调步长次梯度超梯度法

在这项工作中，我们提出了一种自适应投影方法，用于解决真实希尔伯特空间中利普希茨连续和拟单调映射（或没有单调性的利普希茨连续映射）的变分不等式。使用双惯性步骤技术到单投影方法中，我们给出了所提出算法的弱收敛和强收敛定理。本文获得的结果扩展了文献中的一些最新结果。