In this work, we introduce self-adaptive methods for solving variational inequalities with Lipschitz continuous and quasimonotone mapping(or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Under suitable assumptions, the convergence of algorithms are established without the knowledge of the Lipschitz constant of the mapping. The results obtained in this paper extend some recent results in the literature. Some preliminary numerical experiments and comparisons are reported.

中文翻译：

---

求解拟单调变分不等式的迭代方法的弱收敛

在这项工作中，我们介绍了在真实希尔伯特空间中使用Lipschitz连续和拟单调映射（或没有单调性的Lipschitz连续映射）来解决变分不等式的自适应方法。在适当的假设下，无需了解映射的Lipschitz常数即可建立算法的收敛性。本文获得的结果扩展了文献中的一些最新结果。报告了一些初步的数值实验和比较。