Extragradient Method

The extragradient method is an iterative algorithm used to solve variational inequality problems, a broad class encompassing optimization and game theory problems. Current research focuses on extending its application to non-convex and non-concave settings, including Riemannian manifolds and minimax problems, often employing variations like past extragradient and momentum extragradient to improve convergence. These advancements aim to address challenges like escaping limit cycles and handling high-dimensional data efficiently, particularly in areas such as machine learning and semidefinite optimization where low-rank solutions are desirable. The resulting improvements in efficiency and robustness have significant implications for solving large-scale optimization problems in various scientific and engineering domains.