Variational Inequality

Variational inequalities (VIs) are a mathematical framework for modeling problems involving finding equilibrium points, encompassing diverse applications from game theory and optimization to machine learning. Current research heavily focuses on developing and analyzing efficient first-order methods, including extragradient and stochastic gradient descent-ascent algorithms, often incorporating techniques like variance reduction, compression, and adaptive step sizes to improve convergence rates and handle constraints or non-monotone settings. These advancements are crucial for tackling large-scale problems in machine learning and other fields where finding solutions to VIs is computationally challenging, impacting areas such as distributed training, min-max optimization, and game-theoretic modeling.