Comparative Analysis of Two Extragradient Algorithms for Solving Variational Inequalities

In this paper, we explore and compare two extragradient algorithms for solving variational inequalities. Additionally, we introduce a modified extragradient method along with optimization techniques to further enhance algorithm efficiency and precision. The study of these algorithms holds significant importance for solving optimization problems, contributing to better understanding and practical applications. The algorithms typically involve iterative updates where each iteration consists of two projection steps: first predicting the solution at an intermediate point, then correcting it using gradient information. In subsequent sections, we will discuss in detail the underlying principles, implementation processes featuring key steps like gradient computations and projection operations, and optimization methods such as step-size selection strategies and convergence acceleration techniques, aiming to provide readers with comprehensive and in-depth understanding.