Accelerated Gradient Method

Accelerated gradient methods aim to speed up the convergence of gradient descent algorithms used to minimize objective functions, a crucial task in many scientific and engineering fields. Current research focuses on extending these methods to handle non-convex and non-smooth problems, often employing techniques like Nesterov's acceleration, Anderson acceleration, and preconditioning, and analyzing their performance through continuous-time models and novel convergence analyses. These advancements are significant because they improve the efficiency of optimization in machine learning, particularly for training deep neural networks and solving large-scale problems where standard gradient descent is too slow.