In this paper, we introduce a novel Extra-Gradient method with anchor term governed by general parameters. Our method is derived from an explicit discretization of a Tikhonov-regularized monotone flow in Hilbert space, which provides a theoretical foundation for analyzing its convergence properties. We establish strong convergence to specific points within the solution set, as well as convergence rates expressed in terms of the regularization parameters. Notably, our approach recovers the fast residual decay rate $O(k^{-1})$ for standard parameter choices. Numerical experiments highlight the competitiveness of the method and demonstrate how its flexible design enhances practical performance.

翻译：本文提出了一种新型外梯度方法，其锚点项由广义参数控制。该方法源自希尔伯特空间中Tikhonov正则化单调流的显式离散化，这为分析其收敛性质提供了理论基础。我们建立了向解集内特定点的强收敛性，以及用正则化参数表示的收敛速率。值得注意的是，对于标准参数选择，我们的方法恢复了$O(k^{-1})$的快速残差衰减速率。数值实验突显了该方法的竞争力，并展示了其灵活设计如何提升实际性能。