Extra-Gradient Method with Flexible Anchoring: Strong Convergence and Fast Residual Decay

TL;DR

This paper presents a new Extra-Gradient method with flexible anchoring that achieves strong convergence and fast residual decay, supported by theoretical analysis and numerical experiments.

Contribution

It introduces a novel Extra-Gradient algorithm based on Tikhonov regularization, providing strong convergence guarantees and improved residual decay rates.

Findings

Achieves strong convergence to solution points.

Attains residual decay rate of O(k^{-1}).

Demonstrates practical efficiency through numerical tests.

Abstract

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.