Newton's Method Gets a Modern Upgrade: A Faster, Broader Optimization Algorithm
2025-03-25
Over 300 years ago, Isaac Newton developed an algorithm for finding the minimum values of functions. Now, Amir Ali Ahmadi of Princeton University and his students have improved this algorithm to efficiently handle a broader class of functions. This breakthrough uses higher-order derivatives and cleverly transforms the Taylor expansion into a convex sum-of-squares form, achieving faster convergence than traditional gradient descent. While currently computationally expensive, future advancements in computing could allow this algorithm to surpass gradient descent in fields like machine learning, becoming a powerful tool for optimization problems.