Newton Method

Newton's method, a powerful iterative technique for finding roots or optimizing functions, remains a central focus in optimization research, particularly within machine learning and scientific computing. Current research emphasizes improving its efficiency and robustness, especially for high-dimensional problems, through techniques like cubic regularization, variance reduction, and subspace methods (e.g., Krylov subspace methods), as well as addressing challenges in federated learning and privacy. These advancements enhance the applicability of Newton-type methods to large-scale problems, impacting fields ranging from neural network training and PDE solving to multi-objective optimization and robust statistics.