First Newton Based Source

Research on Newton-based methods is addressing the limitations of traditional gradient descent in various optimization problems, particularly in large-scale and distributed settings. Current efforts focus on improving the efficiency and scalability of Newton's method through techniques like Hessian sketching, adaptive resource allocation, and hybrid approaches combining Newton's method with neural networks or other acceleration strategies. These advancements aim to enhance convergence speed and reduce computational costs in applications ranging from federated learning and nonlinear dynamics to robotics control, offering significant improvements over first-order methods in specific contexts. The resulting algorithms demonstrate superior performance in terms of convergence rate and resource efficiency compared to existing methods.